Endurance limit

A method for estimating the endurance limit that avoids the need for long exposure times has been described by Lewis et They used a modified Prot approach in which failure times were determined for joints progressively loaded at several constant rates until failure occurred. They analyzed their results using Eq. (6), derived by Loveless et 

In this equation a is the rate of loading, tb is the time to failure, K is a material constant, Sq is a preload term (or the stress at time t = 0), and EL is the endurance limit. Rearranging Eq. (6) and setting Sq = 0, the usual experimental condition, gives Eq. (7). 

By plotting atl against tt, a straight line is obtained of slope 2EL and intercept 2K. Lewis et al determined the endurance limit for a variety of adhesives (Table IX) and found that the ratio EL/LSS was approximately constant and independent of the value of LSS. Further, the ratio was found 

Allen and Dean have confirmed the findings of Lewis et al and have tested the reliability of prediction of the endurance limit by cyclic durability testing. They have shown that joints prepared with a vinyl-phenolic adhesive were damaged when subjected to a loading cycle above the endurance limit but not when the loading cycle was below the endurance limit. 

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Cumulative Damage. Pressure vessels may be subjected to a variety of stress cycles during service some of these cycles have ampHtudes below the fatigue (endurance) limit of the material and some have ampHtudes various amounts above it. The simplest and most commonly used method for evaluating the cumulative effect of these various cycles is a linear damage relationship in which it is assumed that, if cycles would produce failure at a... 

The data presented in Figure 19.7 were obtained on a Sonntag-Universal machine which flexes a beam in tension and compression. Whereas the acetal resin was subjected to stresses at 1800 cycles per minute at 75°F and at 100% RH, the nylons were cycled at only 1200 cycles per minute and had a moisture content of 2.5%. The polyethylene sample was also flexed at 1200 cycles per minute. Whilst the moisture content has not been found to be a significant factor it has been observed that the geometry of the test piece and, in particular, the presence of notches has a profound effect on the fatigue endurance limit. 

Stainless steels are subject to fatigue failure under dry conditions as are all metallic materials, having distinct fatigue limits where level is dependent on steel type and heat treatment. The limits can be depressed by the simultaneous action of a corrodent, the degree depending upon the nature of the corrodent. Under severe conditions the limit can be displaced to very low values and it is customary to describe resistance by an endurance limit, that is the cyclic stress to give rupture at a specific number of cycles when in contact with a specific corrodent. Some comparative data are in Table 3.25. 

Fig. 8.71 Corrosion fatigue endurance limits for various alloys in aerated salt solutions or...

Fatigue limit dry fatigue (MN/m ) Endurance limit corrosion fatigue, MN/m (10 ) cycles... 

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. 

Cyclic loading significantly reduces the amount of allowable stress a material can withstand. If data are not available on the endurance limit of a material being considered for use, a percentage of its tensile strength can... 

Figure 1.13 Typical fatigue curve (S-N diagram for a material having an endurance limit, oe).

A detailed fatigue analysis is required if any of these conditions is likely to occur to any significant extent. Fatigue failure will occur during the service life of the vessel if the endurance limit (number of cycles for failure) at the particular value of the cyclic stress is exceeded. The codes and standards should be consulted to determine when a detailed fatigue analysis must be undertaken. 

In choosing a spring, the maximum shear stress must not exceed the endurance limit of the material. Table 10.1 lists these two parameters for commonly used spring materials. 

The fatigue life is the number of cycles a specimen can remain at a specified strain or stress before specimen failure occurs. As stress is decreased, there is a point beyond which failure does not occur regardless of the number of cycles the specimen experiences. This stress value is called the endurance limit or endurance strength. 

Fig. 4.1-46. Endurance limit of cross-bored pipe probes.

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