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     Approach to Fatigue Failure in Analysis and Design    Fatigue-Life Methods     The Stress-Life Method     The Strain-Life Method     The Linear-Elastic Fracture Mechanics Method    The Endurance Limit     Fatigue Strength     Endurance Limit Modifying Factors    Stress Concentration and Notch Sensitivity     Characterizing Fluctuating Stresses     Fatigue Failure Criteria for Fluctuating Stress     Torsional Fatigue Strength under Fluctuating Stresses     Combinations of Loading Modes    Varying, Fluctuating Stresses; Cumulative Fatigue Damage     Surface Fatigue Strength     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. 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)

6. Marin’s Equation rotary-beam test specimen endurance limit (7-17)
Endurance limit at the critical location of a machine part in geometry and condition of use
rotary-beam test specimen endurance limit

8. (7-18)
where is the minimum tensile strength and and are to be found in Table 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)

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)
Average
kpsi
MPa
Bending 1
Axial
1.23
1.43
-0.078
0.85
Torsion
0.328
0.258
0.125
0.59
Values given in Textbook

14. (7-26)
where

15. (7-27)
Table 7-6
Effect of operating temperature on the tensile strength of steel.

16. If Reliability is not mentioned Otherwise Use Table 7-7
Table 7-7 Reliability factor Ka corresponding to 8% standard deviation of the endurance limit.
If Reliability is not mentioned
Otherwise Use Table 7-7

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 for reversed bending or reversed axial load for reversed torsion use Fig
For cast iron use q = 0.20 to be conservative.

23. Figure 7-20
and
Figure 7-21:
Notch sensitivity curves.

25. References
Design Theory
Resources
Manufacturing