ME 307 Machine Design I
Dr. A. Aziz Bazoune
King Fahd University of Petroleum & Minerals
Mechanical Engineering Department
Dr. A. Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC 23
Slide 1
ME 307 Machine Design I
Dr. A. Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC 23
Slide 2
ME 307 Machine Design I
7-10 Stress Concentration Factor and Notch
Sensitivity
In fatigue: Stress concentration should always be taken into account.
Dr. A. Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
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Slide 3
ME 307 Machine Design I
Some materials are not fully sensitive to notches and a reduced
value of Kt is used and the maximum stress is calculated as
follows:
(7-29)
Kf is the fatigue stress concentration factor, for simple loading: (Ex 7.7)
or
Dr. A. Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
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Slide 4
ME 307 Machine Design I
Notch sensitivity q index is defined by
(7-30)
0  q 1
To find q use Fig. 7-20 for steel and Al alloys , for reversed bending or
reversed axial load.
For reversed torsion use Fig. 7-21.
For cast iron use q  0.20 to be conservative.
For q  0 , then K f  1 and the material has no sensitivity at notch
at all.
For q  1 , then K f  Kt and the material has full notch sensitivity.
Dr. A. Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC 23
Slide 5
ME 307 Machine Design I
Dr. A. Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC 23
Slide 6
ME 307 Machine Design I
In analysis or design work
Find
first from the geometry of the part
Specify the material
Find
Solve for
from the following Equation
(7-31)
Figure 7-20 has its basis the Neuber equation, which is given by
(7-32)
Where
Dr. A. Bazoune
is defined as the Neuber constant and is a material constant.
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
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Slide 7
ME 307 Machine Design I
Equating Eqs. (7-31) and (7-32) gives the notch sensitivity equation
(7-33)
For steel, with
in kpsi, the Neuber equation can be approximated
by a third polynomial fit of data as
(7-34)
Where
Dr. A. Bazoune
is defined as the Neuber constant and is a material constant.
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC 23
Slide 8
ME 307 Machine Design I
A distinction in the configuration of the notch is accounted for in the
modified Neuber equation (after Heywood), where the fatigue stressconcentration factor
is given as
(7-35)
where Table 7-8
gives values of
for steels for
transverse holes,
shoulders and
grooves.
Dr. A. Bazoune
Table 7-8 Heywood’s Parameter
for steels
Feature
(a)1/2 (in)1/2
Sut in kpsi
(a)1/2 (mm)1/2
Sut in MPa
Transverse hole
5/Sut
174/Sut
Shoulder
4/Sut
139/Sut
Groove
3/Sut
104/Sut
Chapter 7: Fatigue Failure Resulting from variable Loading
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Slide 9
ME 307 Machine Design I
(Textbook)
ka  4.51 520
Dr. A. Bazoune
0.260
 0.859
Chapter 7: Fatigue Failure Resulting from variable Loading
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Slide 10
ME 307 Machine Design I
Dr. A. Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC 23
Slide 11
ME 307 Machine Design I
(Textbook)
SOLUTION
Dr. A. Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC 23
Slide 12
ME 307 Machine Design I
(Textbook)
SOLUTION
Dr. A. Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC 23
Slide 13
ME 307 Machine Design I
Dr. A. Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC 23
Slide 14
ME 307 Machine Design I
(Textbook)
SOLUTION
See next page
Dr. A. Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
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Slide 15
ME 307 Machine Design I
Dr. A. Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
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ME 307 Machine Design I
Dr. A. Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
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Slide 17
ME 307 Machine Design I
a  0.062 in=0.312 mm
With 2.5% lower than a) and b)
Dr. A. Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
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Slide 18