CH07 LEC22 Slide 1

1
Chapter 7
Fatigue Failure Resulting from Variable Loading
Dr. A. Aziz Bazoune King Fahd University of
Petroleum Minerals Mechanical Engineering
Department
2
Chapter Outline
7-1 Introduction to Fatigue in Metals     306
7-2 Approach to Fatigue Failure in Analysis and
Design    312 7-3 Fatigue-Life Methods  
 3137-4 The Stress-Life Method    313 7-5 The
Strain-Life Method    3167-6 The Linear-Elastic
Fracture Mechanics Method    3197-7 The
Endurance Limit    3237-8 Fatigue Strength  
 3257-9 Endurance Limit Modifying Factors   
3287-10 Stress Concentration and Notch
Sensitivity    335 7-11 Characterizing
Fluctuating Stresses    3447-12 Fatigue Failure
Criteria for Fluctuating Stress    346 7-13
Torsional Fatigue Strength under Fluctuating
Stresses    360 7-14 Combinations of Loading
Modes    3617-15 Varying, Fluctuating Stresses
Cumulative Fatigue Damage    3647-16 Surface
Fatigue Strength    3707-17 Stochastic Analysis
   373
3
LECTURE-22
7-9 Endurance Limit Modifying Factors 7-10 Stress
Concentration and Notch Sensitivity
4
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

5
Marins Equation   

• Marin identified factors that quantified the
  effects of
• surface condition
• size
• loading
• temperature
• miscellaneous items

Marins Equations is therefore written as
(7-17)
6
Marins Equation   
(7-17)
Endurance limit at the critical
location of a machine part in geometry and
condition of use rotary-beam test specimen
endurance limit
7
(No Transcript)
8
(7-18)
where is the minimum tensile strength and
and are to be found in Table 7-4. Notice
that and 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)
9
(No Transcript)
10
The size factor for bending and torsion may
be given by
(7-19)
For axial loading there is no size effect, so
(7-20)
11
Non-Rotating Parts

• If a round bar in bending is not rotating or when
  a non-circular 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
  with the similarly stressed area of a rotating
  beam specimen and obtain the effective
  diameter 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.
12
Table 7-5 Areas of common non-rotating
structural shapes
Use de Eq. (7-23) for round and Eq.(7-24) for
rectangular cross-sections
13
General form of load factor
(7-25)
Values given in Textbook
14
(7-26)
15
(7-27)
Table 7-6 Effect of operating temperature on the
tensile strength of steel.
16
Table 7-7 Reliability factor Ka corresponding to
8 standard deviation of the endurance limit.
17

• Residual stresses
• Directional characteristics
• (e.g. rolling, drawing)
• Corrosion
• Plating
• Metal spraying
• Frequency of cycling
• Fretting corrosion

18
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)
19
7-10 Stress Concentration Factor and Notch
Sensitivity    
20
7-10 Stress Concentration Factor and Notch
Sensitivity    
In fatigue Stress concentration should always be
taken into account.
21
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
22
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.

23
Figure 7-20 and Figure 7-21 Notch sensitivity
curves.
24
(No Transcript)
25

• 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.as
  p?catId373
• http//www.engineersedge.com/
• http//www.bearings.machinedesign.com/guiEdits/Con
  tent/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/pro
  cess.cfm
• http//www.me.gatech.edu/jonathan.colton/me4210/mf
  gvideos.html