LEC 22 CH-07 - KFUPM Open Courseware
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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-07
LEC-22
Slide - 1
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-07
LEC-22
Slide - 2
ME 307 Machine Design I
7-9 Endurance Limit Modifying Factors
7-10 Stress Concentration and Notch Sensitivity
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC-22
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ME 307 Machine Design I
7-9
Endurance Limit Modifying Factors
The rotating-beam specimen used in the laboratory to determine endurance limits is
prepared very carefully and tested under closely controlled conditions. It is unrealistic to
expect the endurance limit of a mechanical or structural member to match the values
obtained in the laboratory. Some differences include
Material: composition, basis of failure, variability
Manufacturing: method, heat treatment, fretting corrosion, surface condition, stress
concentration
Environment: corrosion, temperature, stress state, relaxation times
Design: size, shape, life, stress state, stress concentration, speed, fretting, galling
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC-22
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ME 307 Machine Design I
Marin’s Equation
Marin identified factors that quantified the effects of
surface condition
size
loading
temperature
miscellaneous items
Marin’s Equations is therefore written as:
(7-17)
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC-22
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ME 307 Machine Design I
Marin’s Equation
(7-17)
Se :
Endurance limit at the critical location of a machine part in geometry
and condition of use
S 'e :
rotary-beam test specimen endurance limit
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC-22
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ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC-22
Slide - 7
ME 307 Machine Design I
(7-18)
where Sut is the minimum tensile strength and
Notice that
a and b
a and b
are to be found in Table 7-4.
are different from those given by Eqs. (7-13) and (7-14)
respectively.
Table 7-4
Parameters for Marin
surface modification
factor, Eq. (7-18)
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC-22
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ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC-22
Slide - 9
ME 307 Machine Design I
k
The size factor b for bending and torsion may be given by:
(7-19)
For axial loading there is no size effect, so
(7-20)
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC-22
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ME 307 Machine Design I
Non-Rotating Parts
If a round bar in bending is not rotating or when a noncircular cross-section is used what is kb ?
Assume that fatigue damage occurs in material that is
stressed above 95% of its maximum stress.
Equate the portion of a non-round part stressed
max
with the similarly stressed area of a rotating beam
specimen and obtain the effective diameter
de
where.
(7-23)
as the effective size of a round corresponding to a non-rotating solid
or hollow round. Table 7-5 provides areas of common structural
shapes undergoing non-rotating bending.
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC-22
Slide - 11
ME 307 Machine Design I
Table 7-5
Areas of common non-rotating structural shapes
Use
Dr. A. Aziz Bazoune
de
Eq. (7-23) for round and Eq.(7-24) for rectangular cross-sections
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC-22
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ME 307 Machine Design I
General form of load factor
(7-25)
kc
kpsi
MPa
1
1
0
1
Axial
1.23
1.43
-0.078
0.85
Torsion
0.32
8
0.258
0.125
0.59
Bending
Average
Values given in Textbook
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC-22
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ME 307 Machine Design I
kd 0.975 0.432 103 TF 0.115 105 TF2
0.104 10
where
8
T
3
F
0.595 10
12
T
(7-26)
4
F
70 TF 1000 F
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC-22
Slide - 14
ME 307 Machine Design I
(7-27)
Table 7-6
Effect of operating
temperature on the
tensile strength of
steel.
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC-22
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ME 307 Machine Design I
If Reliability is not mentioned
Otherwise Use Table 7-7
Dr. A. Aziz Bazoune
Table 7-7 Reliability factor Ka
corresponding to 8% standard deviation
of the endurance limit.
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
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ME 307 Machine Design I
Residual stresses
Directional characteristics
(e.g. rolling, drawing)
Corrosion
Plating
Metal spraying
Frequency of cycling
Fretting corrosion
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
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ME 307 Machine Design I
7-10 Stress Concentration Factor and Notch Sensitivity
In Chapter 4, it was pointed out that: The existence of irregularities or
discontinuities, such as holes, grooves or notches, in a part increases the
theoretical stresses significantly in the immediate vicinity of discontinuity.
(4-48)
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
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ME 307 Machine Design I
7-10 Stress Concentration Factor and Notch Sensitivity
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC-22
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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. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC-22
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ME 307 Machine Design I
7-10 Stress Concentration Factor and Notch Sensitivity
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. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
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ME 307 Machine Design I
Notch sensitivity q index is defined by
(7-39)
q for steel and Al alloys are given in Fig. 7-20 for reversed
bending or reversed axial load for reversed torsion use Fig. 7.21.
For cast iron use q = 0.20 to be conservative.
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
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ME 307 Machine Design I
Figure 7-20
and
Figure 7-21:
Notch
sensitivity
curves.
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC-22
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ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC-22
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ME 307 Machine Design I
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References
Design Theory
http://deseng.ryerson.ca/DesignScience/
http://www-3.ibm.com/ibm/easy/eou_ext.nsf/Publish/6
Resources
http://www.machinedesign.com/ASP/enggMechanical.asp?catId=373
http://www.engineersedge.com/
http://www.bearings.machinedesign.com/guiEdits/Content/BDE_6_4/bdemech_a02.aspx
http://icrank.com/cgi-bin/pageman/pageout.cgi?path=/index_html.html
Manufacturing
http://www.efunda.com/processes/processes_home/process.cfm
http://www.me.gatech.edu/jonathan.colton/me4210/mfgvideos.html
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from variable Loading
CH-07
LEC-22
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