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Title: CH-07 LEC-21 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-21
7-7 The Endurance Limit    7-8 Fatigue
Strength   7-9 Endurance Limit Modifying
Factors
4
7-7 The Endurance Limit   
  • A quick method of estimating endurance limits is
    needed
  • for preliminary and prototype design
  • for some failure analysis
  • Experimental results for
  • rotating-beam tests
  • simple tension tests
  • of specimens taken from
  • the same bar are shown in
  • Figure 7.18.

Figure 7-18 Graph of endurance limits versus
tensile strengths from actual test results for a
large number of wrought irons and steels.
5
Figure 7-18 Graph of endurance limits versus
tensile strengths from actual test results for a
large number of wrought irons and steels. Ratios
of Se/Sut of 0.60, 0.50, and 0.40 are shown by
the solid and dashed lines. Note also the
horizontal dashed line for of Se107 kpsi.
Points shown having a tensile strength greater
than 214 kpsi have a mean endurance limit of
Se107 kpsi and a standard deviation of 13.5
kpsi.
6
  • For steels, the relationship between the tensile
    strength and the endurance limit is given by

(7-8)
  • where
  • is the minimum tensile strength. The prime
    mark on in this equation refers to the
    rotating-beam specimen itself.
  • The unprimed symbol is for the
    endurance limit of any particular machine element
    subjected to any kind of loading.

7
The endurance limits for various classes of cast
irons, polished or machined, are given in Table
A-24. Aluminum alloys do not have an endurance
limit. The fatigue strengths of some aluminum
alloys at 5(108 ) cycles of reversed stress are
given in Table A-24.
8
7-7 Fatigue Strength   
  • Region of low cycle fatigue
  • The fatigue strength is only slightly
    smaller than the tensile
  • strength .
  • Region of high Cycle Fatigue
  • The purpose of this section is to develop
    methods of approximation of the S-N diagram in
    the high-cycle region, when information may be as
    sparse as the results of a simple tension test.
    Experience has shown high-cycle fatigue data are
    rectified by a logarithmic transform to both
    stress and cycles-to-failure.

9
7-8 Fatigue Strength   
In the region of high cycle fatigue, the equation
relating the fatigue strength to the number
of cycles to failure may be given by the
empirical curve fit equation where is
the number of cycles to failure and a and b are
given by
(7-12)
(7-13)
(7-14)
where is found from Figure 7-19.
10
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11
(7-15)
12
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13
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14
Example  
Given a 1050 HR steel, estimate a) The
rotating-beam endurance limit at 106. b) The
endurance strength of a polished rotating beam
specimen corresponding to 104 cycles to
failure. c) The expected life of a polished
rotating-beam specimen under a completely
reversed stress of 55 kpsi.
SOLUTION a) From Table A-20,
From Eq. (7-8) b) From Fig. (7-19) for

15
Example (Cont.d)  
From Eq. (7-13) and (7-14) ?
Thus Eq. (7-12) is for
cycles to failure, the above equation
becomes
16
Example (Cont.d)  
c) From Eq. (7-15), with
Keep in mind that these are only
estimates.
17
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

18
Marins Equation   
Marin identified factors that quantified the
effects of surface condition, size, loading,
temperature, and miscellaneous items. Marins
Equations is therefore written as
(7-17)
Endurance limit at the critical
location of a machine part in geometry and
condition of use rotary-beam test specimen
endurance limit
19
When endurance tests of parts are not available,
estimations are made by applying Marin factors to
the endurance limit.
20
(7-18)
where is the minimum tensile strength and
and are to be found in Table 7-4.
Table 7-4 Parameters for Marin surface
modification factor, Eq. (7-18)
21
The size factor for bending and torsion may
be given by
(7-19)
For axial loading there is no size effect, so
(7-20)
22
QUESTION What to do with Eq.(7-19) if a round
bar in bending is not rotating or when a
non-circular cross-section is used?
ANSWER Use effective dimension 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
23
Table 7-5 Areas of common non-rotating
structural shapes
24
Average values for the load factor are given by

(7-25)
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