13-6] 



VIBRATION AND SHOCK 



701 



Endurance Limit 



cyclic stress, that is, under vibration, as distinguished from their behavior 

 under steady stress. It is well established that metals can be made to fail 

 under the action of cyclic stress even though the maximum stress of the 

 cycles is far below their static breaking strength. Fatigue failure appears 

 to start with the development of a crack in or near the surface of a part. 

 Under the influence of the cyclic stress, this crack propagates steadily 

 through the part until the remaining material is unable to sustain the 

 maximum load. At this instant, a rapid failure occurs. 



Design for cyclic stresses depends, 

 in part, upon the results of fatigue 

 tests made upon numerous identical 

 specimens of the material in ques- 

 tion. The usual graphical presenta- 

 tion of these results is known as an 

 S-N diagram. One form of S-N 

 diagram is shown in Fig. 13-10. 

 Here the logarithm of the maximum 

 stress in a load cycle is plotted 

 versus the logarithm of the number 

 of cycles required to produce a 



failure. Many materials, when tested, give a curve similar in shape to that 

 shown in Fig. 13-10. The stress corresponding to the horizontal part of the 

 diagram is called the endurance limit for the conditions of the test. It is 

 evident from inspection of the figure that for parts which may be stressed 

 above their endurance limits, there is a relationship between peak cyclic 

 stress (or vibration amplitude) and probable life. The S-N diagram gives 

 this relationship for the specimens tested. Application to an actual design 

 may require consideration of many additional factors affecting the fatigue 

 strength of a part. Some of these are now listed: 



Overstressing (before service) 

 Other environmental factors — 

 temperature, atmosphere, ex- 

 ternal pressure, etc. 

 Surface finish 



LOG NUIVIBER OF LOAD CYCLES 



Fig. 13-10 S-N Diagram. 



1. Mean stress 



2. Residual stress 



3. Size of specimen 



4. Stress concentration 



5. Frequency of stress cycle 



6. Heat treatment of specimen 



10. 



1 1 . Surface cold work 



7. Understressing (before service) 12. Surface coating or treatment 



Analytical design for vibration is further complicated by the fact that 

 the available data on fatigue characteristics of metals are based upon 

 sinusoidal tests and therefore require interpretation before being applied 

 to random stresses. 



If an environment with severe vibration is expected, the avoidance of 

 damage will require a design based upon consideration of the expected 



