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					   Chapter 7: Failure Prediction for
     Cyclic and Impact Loading


                              All machines and
                              structural designs are
                              problems in fatigue
                              because the forces of
                              Nature are always at work
                              and each object must
                              respond in some fashion.

                              Carl Osgood, Fatigue
                              Design




Hamrock • Fundamentals of Machine Elements
                         On the Bridge!




Figure 7.1 “On the Bridge”, an illustration from Punch magazine in
1891 warning the populace that death was waiting for them on the next
bridge. Note the cracks in the iron bridge.
         Hamrock • Fundamentals of Machine Elements
                   Methods to Maximize Design Life


1.   By minimizing initial flaws, especially surface flaws. Great care is taken to produce fatigue-
     insusceptible surfaces through processes, such as grinding or polishing, that leave
     exceptionally smooth surfaces. These surfaces are then carefully protected before being placed
     into service.
2.   By maximizing crack initiation time. Surface residual stresses are imparted (or at least tensile
     residual stresses are relieved) through manufacturing processes, such as shot peening or
     burnishing, or by a number of surface treatments.
3.   By maximizing crack propagation time. Substrate properties, especially those that retard crack
     growth, are also important. For example, fatigue cracks propagate more quickly along grain
     boundaries than through grains (because grains have much more efficient atomic packing).
     Thus, using a material that does not present elongated grains in the direction of fatigue crack
     growth can extend fatigue life (e.g., by using cold-worked components instead of castings).
4.   By maximizing the critical crack length. Fracture toughness is an essential ingredient. (The
     material properties that allow for larger internal flaws are discussed in Chapter 6.)




               Hamrock • Fundamentals of Machine Elements
          Stress Cycle and Test Specimen




                                  Figure 7.3 R.R. Moore
Figure 7.2 Variation in nonzero
                                  machine fatigue test specimen.
cyclic mean stress.
                                  Dimensions in inches.


      Hamrock • Fundamentals of Machine Elements
                Cyclic Properties of Metals




Table 7.1 Cyclic properties of some metals.

         Hamrock • Fundamentals of Machine Elements
                     Fatigue Crack Growth




Figure 7.4 Illustration of fatigue crack growth. (a) Size of a fatigue
crack for two different stress ratios as a function of the number of
cycles; (b) rate of crack growth, illustrating three regimes.

         Hamrock • Fundamentals of Machine Elements
     Fatigued Part Cross-Section




                          Figure 7.5 Cross-section of a
                          fatigued section, showing
                          fatigue striations or beachmarks
                          originating from a fatigue crack
                          at B.




Hamrock • Fundamentals of Machine Elements
                         Fatigue Fracture Surfaces




                            Figure 7.6 Typical fatigue
                            fracture surfaces of smooth and
                            notched cross-sections under
                            different loading conditions and
                            stress levels.

Hamrock • Fundamentals of Machine Elements
       Fatigue Strength of Ferrous Metals




Figure 7.7 Fatigue strengths as a function of number of loading
cycles. (a) Ferrous alloys, showing clear endurance limit.


     Hamrock • Fundamentals of Machine Elements
      Fatigue Strength of Aluminum Alloys




Figure 7.7 Fatigue strengths as a function of number of loading
cycles. (b) Aluminum alloys, with less pronounced knee and no
endurance limit.
     Hamrock • Fundamentals of Machine Elements
           Fatigue Strengths of Polymers




Figure 7.7 Fatigue strengths as a function of number of loading
cycles. (c) Selected properties of assorted polymer classes.
      Hamrock • Fundamentals of Machine Elements
      Endurance Limit vs. Ultimate Strength




Figure 7.8 Endurance limit as function of ultimate strength for
wrought steels.
       Hamrock • Fundamentals of Machine Elements
                Endurance Limit




Table 7.2 Approximate endurance limit for various
materials.



 Hamrock • Fundamentals of Machine Elements
                     Notch Sensitivity




                                                       Usage:




Figure 7.9 Notch sensitivity as function of notch radius for
several materials and types of loading.
     Hamrock • Fundamentals of Machine Elements
                   Surface Finish Factor




                                    Table 7.3 Surface finish factor.


Figure 7.10 Surface finish factors for
steel. (a) As function of ultimate strength
in tension for different manufacturing
processes.
            Hamrock • Fundamentals of Machine Elements
  Roughness Effect on Surface Finish Factor




Figure 7.10 Surface finish factors for steel. (b) As function of
ultimate strength and surface roughness as measured with a stylus
profilometer.
      Hamrock • Fundamentals of Machine Elements
                   Reliability Factor




Table 7.4 Reliability factor for six probabilities of survival.




   Hamrock • Fundamentals of Machine Elements
                         Shot Peening




Figure 7.11 The use of shot peening to improve fatigue
properties. (a) Fatigue strength at two million cycles for high
strength steel as a function of ultimate strength; (b) typical S-N
curves for nonferrous metals.
      Hamrock • Fundamentals of Machine Elements
                       Example 7.4




Figure 7.12 Tensile loaded bar. (a) Unnotched; (b) notched.



     Hamrock • Fundamentals of Machine Elements
          Influence of Non-Zero Mean Stress

                                         Gerber Line




                                        Goodman Line




                                       Soderberg Line

Figure 7.13 Influence of nonzero
mean stress on fatigue life for tensile
loading as estimated by four empirical
relationships.
           Hamrock • Fundamentals of Machine Elements
     Modified Goodman Diagram




                     Figure 7.14 Complete modified
                     Goodman diagram, plotting stress as
                     ordinate and mean stress as abscissa.



Hamrock • Fundamentals of Machine Elements
     Modified Goodman Criterion




                              Table 7.5 Equations and
                              range of applicability for
                              construction of complete
                              modified Goodman
                              diagram.




Hamrock • Fundamentals of Machine Elements
         Modified Goodman Criterion




Table 7.6 Failure equations and validity limits of equations
for four regions of complete modified Goodman diagram.



  Hamrock • Fundamentals of Machine Elements
               Example 7.7




Figure 7.15 Modified Goodman diagram for
Example 7.7.

Hamrock • Fundamentals of Machine Elements
     Alternating Stress Ratio for Cast Iron




Figure 7.16 Alternating stress ratio as function of mean stress
ratio for axially loaded cast iron.



  Hamrock • Fundamentals of Machine Elements
                Properties of Mild Steel




Figure 7.17 Mechanical properties of mild steel at room
temperature as a function of strain rate.

         Hamrock • Fundamentals of Machine Elements
                       Example 7.10




Figure 7.18 Diver impacting diving board, used in Example 7.10.
(a) Side view; (b) front view; (c) side view showing forces and
coordinates.

        Hamrock • Fundamentals of Machine Elements
 Brake Stud Design Analysis




Figure 7.19 Dimensions of existing
                                 Figure 7.20 Press brake stud loading.
brake drum design.               (a) Shear and bending-moment
                                 diagrams for applied load; (b) stress
                                 cycle.
           Hamrock • Fundamentals of Machine Elements

				
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posted:10/27/2011
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