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530.352 Materials Selection. Lecture #23 Fatigue Tuesday November 8 th , 2005. Failure even at low Stresses. Failure often occurs even when:  applied <  fracture and  applied <  yielding 90% of all mechanical failures are related to dynamic loading.

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530 352 materials selection l.jpg

530.352 Materials Selection

Lecture #23 FatigueTuesday November 8th, 2005


Failure even at low stresses l.jpg

Failure even at low Stresses

  • Failure often occurs even when:applied < fractureand applied < yielding

  • 90% of all mechanical failures are related todynamic loading.

  • Dynamic Loading -> Cyclic Stresses


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Examples of Fatigue Failures

Plastic Tricycle:


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Examples of Fatigue Failures

Door Stop:


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Versailles 1842

first fatigue problem

axial failure

Today

flaws in 10% of rails.

Examples of Fatigue Failures

Railway Accidents:


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Types of Fatigue

  • Fatigue of uncracked components

    • No pre-cracks; initiation controlled fracture

    • Examples : most small components: pins, gears, axles, ...

  • High cycle fatigue

    • fatigue < yield ; Nf > 10,000

  • Low cycle fatigue

    • fatigue > yield ; Nf < 10,000


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Types of Fatigue:

  • Fatigue of cracked structures

    • Pre-cracks exist: propagation controls fracture

    • Examples : most large components, particularly those containing welds: bridges, airplanes, ships, pressure vessels, ...


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Cyclic Loading

Weight

+

time

-


Basic fatigue terminology l.jpg

+

max

mean



0

time

min

-

Basic Fatigue Terminology:

maxmin

mean maxmin

amplitudemaxmin

N = number of fatigue cycles

Nf = number of cycles

to failure


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High Cycle Fatigue

  • Apply controlled applied < ~ 2/3yield

  • Stress is elasticon gross scale.

  • Locally the metal deforms plastically.

S-N Curves

Mild Steel

50

40

30

10

0

Fatigue limit

Stress

Al alloys

105 106 107 108 109

Nfailure


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Low Cycle Fatigue

  • Apply controlled amounts of total

    • total = elastic + plastic

  • Empirical Observations and Rules

    • Coffin-Manson Law

    • Miner’s Rule


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Coffin-Manson Law

For low cycle fatigue:

plastic Nfailure1/2 = Const.

log pl

y=y/E

~104

log Nfailure


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Miner’s Rule

Rule of Accumulative damage:

Ni

Nfailure@ i

= 1

N1

N2

N3

Fraction of life time @ i


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The Fatigue Process

  • Crack initiation

    • early development of damage

  • Stage I crack growth

    • deepening of initial crack on shear planes

  • Stage II crack growth

    • growth of well defined crack on planes normal to maximum tensile stress

  • Ultimate Failure


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Crack initiation

Cracks start at:

• Surfaces

• Inclusions

• Existing cracks

Alternate stresses -> slip bands -> surface rumpling


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Crack Initiation:


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Crack Growth

Striation indicating

steps in crack

advancement.


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Propagation in Cracked Structures

ao~ adetectible < acritical

ao -> acritical = FAILURE !!!

K = Kmax - Kmin

= (a)1/2

da = A1KmdN

Fast fracture

log da/dN

threshold

linear

log K


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Real world comparisons:

Fast fracture

log da/dN

threshold

linear

log K


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Fracture surfaces:


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Fracture Surfaces:

Initiation

site

Fatigue

cracking

Final fracture


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