ME 307 Machine Design I
Dr. A. Aziz Bazoune
King Fahd University of Petroleum & Minerals
Mechanical Engineering Department
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
LEC 20
Slide1
ME 307 Machine Design I
7-1 Introduction to Fatigue in Metals 306
7-2 Approach to Fatigue Failure in Analysis and Design 312
7-3 Fatigue-Life Methods 313
7-4 The Stress-Life Method 313
7-5 The Strain-Life Method 316
7-6 The Linear-Elastic Fracture Mechanics Method 319
7-7 The Endurance Limit 323
7-8 Fatigue Strength 325
7-9 Endurance Limit Modifying Factors 328
7-10 Stress Concentration and Notch Sensitivity 335
7-11 Characterizing Fluctuating Stresses 344
7-12 Fatigue Failure Criteria for Fluctuating Stress 346
7-13 Torsional Fatigue Strength under Fluctuating Stresses 360
7-14 Combinations of Loading Modes 361
7-15 Varying, Fluctuating Stresses; Cumulative Fatigue Damage 364
7-16 Surface Fatigue Strength 370
7-17 Stochastic Analysis 373
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
LEC 20
Slide2
ME 307 Machine Design I
7-1
7-2
7-3
7-3
Dr. A. Aziz Bazoune
Introduction to Fatigue in Metals
Approach to Fatigue Failure in Analysis and
Design
Fatigue-Life Methods
The Stress-Life Method
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
LEC 20
Slide3
ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
LEC 20
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ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
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ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
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ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
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ME 307 Machine Design I

Crack Initiation
 Fatigue always begins at a crack
 Crack may start at a microscopic
inclusion (<.010 in.)
 Crack may start at a "notch", or
other stress concentration

Crack Propagation
 Sharp crack creates a stress
concentration
 Each tensile stress cycle causes
the crack to grow
(~10-8 to 10-4 in/cycle)

Fracture
 Sudden, catastrophic failure
with no warning.
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
LEC 20
Slide8
ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
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ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
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ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
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ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
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ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
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ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
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ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
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ME 307 Machine Design I
Figure 7-5
Fatigue fracture surface
of a forged connecting
rod of AISI 8640 steel.
The fatigue crack origin
is at the left edge, at the
flash line of the forging,
but no unusual roughness
of the flash trim was
indicated. The fatigue
crack progressed halfway
around the oil hole at the
left, indicated by the
beach marks, before final
fast fracture occurred.
Note the pronounced shear lip in the final fracture at the right edge. (From ASM Handbook,
Vol. 12: Fractography, ASM International, Materials Park, OH 44073-0002, fig 523, p. 332.
Reprinted by permission of ASM International® , www.asminternational.org.)
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
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Slide16
ME 307 Machine Design I
Figure 7-6
Fatigue fracture surface of a 200mm (8-in) diameter piston rod of
an alloy steel steam hammer used
for forging. This is an example of
a fatigue fracture caused by pure
tension where surface stress
concentrations are absent and a
crack may initiate anywhere in
the cross section. In this instance,
the initial crack formed at a
forging flake slightly below
center, grew outward
symmetrically, and ultimately
produced a brittle fracture
without warning. (From ASM
Handbook, Vol.12: Fractography,
ASM International, Materials Park,
OH44073-0002, fig 570, p. 342.
Reprinted by permission of ASM
International,
www.asminternational.org.)
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
LEC 20
Slide17
ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
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Slide18
ME 307 Machine Design I
Figure 7-6
Fatigue failure of an ASTM A186 steel double-flange trailer wheel caused by stamp marks.
(b) Stamp mark showing heavy impression and fracture extending along the base of the lower
row of numbers. (From ASM Handbook, Vol.11: Failure Analysis and Prevention, ASM
International, Materials Park, OH 44073-0002, fig 51, p. 130. Reprinted by permission of ASM
International , www.asminternational.org.)
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
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Slide19
ME 307 Machine Design I
Figure 7-8
Aluminum alloy 7075-T73 landinggear torque-arm assembly redesign
to eliminate fatigue fracture at a
lubrication hole. (a) Arm
configuration, original and
improved design (dimensions given
in inches). (From ASM Handbook,
Vol. 11: Failure Analysis and
Prevention, ASM International,
Materials Park, wall
OH 44073-0002, fig 23, p. 114.
Reprinted By permission of ASM
International,
www.asminternational.org.)
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
LEC 20
Slide20
ME 307 Machine Design I
Figure 7-8
Aluminum alloy 7075-T73 landinggear torque-arm assembly redesign
to eliminate fatigue fracture at a
lubrication hole. (b) Fracture
surface where arrows indicate
multiple crack origins.
(From ASM Handbook, Vol. 11:
Failure Analysis and Prevention,
ASM International, Materials Park,
wall OH 44073-0002, fig 23, p.
114. Reprinted By permission of
ASM International,
www.asminternational.org.)
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
LEC 20
Slide21
ME 307 Machine Design I


Thus far we’ve studied STATIC FAILURE of machine elements.
The second major class of component failure is due to DYNAMIC LOADING
 Repeated stresses
 Alternating stresses
 Fluctuating stresses



The ultimate strength of a material (Su) is the maximum stress a material
can sustain before failure assuming the load is applied only once and
held.
Fatigue strength Resistance of a material to failure under cyclic loading.
A material can also FAIL by being loaded repeatedly to a stress level that
is LESS than (Su)
 Fatigue failure
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
LEC 20
Slide22
ME 307 Machine Design I

Fatigue-Life Methods

Fatigue Strength and the Endurance Limit

Endurance Limit Modifying Factors

Stress Concentration and Notch Sensitivity

Fluctuating Stresses

Combinations of Loading Modes

Varying, Fluctuating Stresses; Cumulative Fatigue Damage
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
LEC 20
Slide23
ME 307 Machine Design I
Three major fatigue life methods used in design and analysis for safe
life estimation:
1.
Stress life method (S-N Curves)
2.
Strain life method (ε-N Curve)
3.
Linear elastic fracture mechanics method
The above methods predict the life in number of cycles to failure, N,
for a specific level of loading. :
1.
Low cycle Fatigue: 1 
2.
High cycle fatigue
Dr. A. Aziz Bazoune
N  103 cycles
N  103 cycles
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
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ME 307 Machine Design I
1. Stress-Life Method

based on stress levels only

It is the least accurate approach, especially for low-cycle
applications.

Most traditional method:

easiest to implement for a wide range of design applications

ample supporting data

represents high-cycle applications adequately
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
LEC 20
Slide25
ME 307 Machine Design I
2. Strain-Life Method

Involves more detailed analysis of the plastic deformation at localized
regions where the stresses and strains are considered for life
estimates.


Good for low-cycle fatigue applications.
Some uncertainties exist in the results.
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
LEC 20
Slide26
ME 307 Machine Design I
3.
Fracture Mechanics Method

Assumes a crack is already present and detected.

Predicts crack growth with respect to stress intensity.

Most practical when applied to large structures in conjunction with
computer codes and a periodic inspection program.
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
LEC 20
Slide27
ME 307 Machine Design I
To determine the strength of materials under the action of fatigue loads, specimens are
subjected to repeated or varying forces of specified magnitudes while the cycles or
stress reversals are counted to destruction. The most widely used fatigue-testing device
is the R. R. Moore high-speed rotating-beam machine. The specimen, shown in
Fig.6-9, is very carefully machined and polished, with a final polishing in an axial
Direction to avoid circumferential scratches.
Figure 7-9
Test-specimen geometry for
the R. R. Moore rotatingbeam machine. The bending
moment is uniform over the
curved at the highest-stressed
portion, a valid test of
material, whereas a fracture
elsewhere (not at the higheststress level) is grounds for
suspicion of material flaw.
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
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ME 307 Machine Design I
R. R. Moore rotating-beam fatigue testing machine
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
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ME 307 Machine Design I
R. R. Moore rotating-beam fatigue testing machine
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
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ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
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ME 307 Machine Design I
There are essentially two types of fatigue:
1.
High Cycle Fatigue (HCF) (Elastic Strain)
2.
Low Cycle Fatigue (LCF) (Plastic Strain)
Semi-Log Scale
The fatigue strength
Sf is the stress level
that a material can
endure for N cycles.
The stress level at
which that material
can withstand an
infinite number of
cycles is called the
endurance limit.
The endurance limit
is observed as a
horizontal line on the
S-N curve.
Endurance Limit (Se):
Maximum stress that a
material will endure
without failure for an
infinite number of load
cycles.
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
LEC 20
Slide32
ME 307 Machine Design I

S-N Curves for Non-Ferrous Metals (Al-Alloys)
Note that nonferrous materials
often exhibit no
endurance limit.
 Eventually these
materials will fail
due to repeated
loading.
 To come up with an
equivalent
endurance limit,
designers typically
use the value of the
fatigue strength Sf
at 108 cycles
Figure 7-11
S-N bands for representative aluminum alloys, excluding
wrought alloys with Sut< 38 kpsi.
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
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ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
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ME 307 Machine Design I
S-N Curves for Polymers
Note that non-ferrous materials often exhibit no
endurance limit.
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
LEC 20
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ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
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ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-7
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Slide37