S-N Curves Endurance Limit

One of the most frequently used tests for fatigue-resistance evaluation is the well-known plotting of stress versus the number of cycles, usually referred to as the S-N (curve) relation . Various wave forms of cyclic stresses may be applied to a specimen to test its suitability to withstand prolonged strain. Machine elements are assessed to determine their practical endurance of industrial applications to which they may be exposed. Such tests focus on the nominal stress required to cause fatigue failure at some number of cycles. A logarithmic scale is almost always used for N, the number of cycles to failure. A schematic S-N plot is shown in Fig. 7.1. Note the horizontal line in plot (a), known as a knee , which represents the endurance limit . As implied by its name, at this level of stress, the specimen is characterized by its ability to endure a large number of stress-cycles at the stress level of the horizontal line and below it without failure. In plot (b), no such horizontal line is observed and the curve continues to decrease, indicating that the stress must be reduced for the test specimen to be able to withstand a certain number of cycles. 

The time to failure may be computed numerically for any time-dependent applied stress function  

In another illustration (Fig. 7.5), an S-N type curve is illustrated for Si3N4. Here, as in Fig. 7.3, static and cyclic fatigue are compared. Typical fractographs for cyclic and static fatigue specimens are shown in Fig. 7.6a, b, respectively. In 

A high-magnification SEM fractograph of the portion between the two semicircular marks in the cyclic fatigue specimen is shown in Fig. 7.6c, after 

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Fatigue data are normally presented as a plot of the stress (S) versus the number of cycles (N) that cause failure at that stress the data plotted defined as an S-N curve (Fig. 2-43). The use of an S-N curve is used to establish a fatigue endurance limit strength. The curve asymptotically approaches a parallel to the abscissa, thus indicating the endurance limit as the value that will produce failure. Below this limit the material is less susceptible to fatigue failure. 

Fig. 2-43 S-N curve establishes fatigue endurance limit strength.

Two conclusions can be drawn from an inspection of the S-N curve (1) the higher the applied material stress or strain, the fewer cycles the specimen can survive and (2) the curve gradually approaches a stress or strain level called the fatigue endurance limit below which the material is much less susceptible to fatigue failure. Different materials may... 

Endurance limit To develop S-N curves the fatigue specimen is loaded until, for example, the maximum stress in the sample is 275 MPa (40 ksi) (Fig. 2-43). At this stress level it may fail in only 10 cycles. These data are recorded and the stress level is then reduced to 206 MPa (30 ksi). Tliis specimen may not break until after 1,000 stress cycles at this rather low stress level. 

Dynamic fatigue b more widefy recognized as a cause of firacture, and most handbools provide fritigue data in the form of S-N curves, as iUustrated in Figure 8.20. These curves usualfy flatten b ond 10 les, in which case it b possible to define a fatigue endurance limit, le. the minimum stress required to cause failure within 10 cycles. Both the static... 

Fig. 7.1 S-N curves a with a well-defined endurance limit, b without a definite fatigue limit...

Dynamic fatigue is more widely recognized as a cause of fracture, and most handbooks provide fatigue data in the form of S-N curves, as illustrated in Fig. 8.20. These curves usually flatten out beyond 10 cycles, in which case it is possible to define a fatigue endurance limit, i.e. the minimum st ress required to cause failure within 10 cycles. Both the static and the dynamic tests reflect the response of the material to the small defects that are present in the unnotched specimens, and in a sense are measuring the distribution of intrinsic flaw sizes as much as the fracture resistance of the polymer. Consequently, when the component is to be used in a critical application, there is a good case for mounting a full-scale fracture mechanics study. 

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