S/N curve

Fig. 2-23 S-N curves for plain carbon steel in 0.05 M potassium hydrogen benzoate (pH 4) at 30°C at various potentials U U = rest potential).

The importance of the prevailing corrosion conditions in determining corrosion fatigue strength is further emphasised by the response of the S-N curve to electrochemical potential and in some instances corrosion... 

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.

Since fatigue cracks often start at a random surface imperfection, considerable scatter occurs in fatigue data, increasing with the increasing lifetime wherever crack initiation occupies most of the fatigue life of a specimen. When a line of the best fit is drawn from the available data points on an S-N curve, this represents the mean life expected at any given stress level or the stress that would cause, say, 50% of the product failures in a given number of cycles. 

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. 

The thin-wall bellows element should be designed for membrane stresses to conform to code-allowable stresses. The sum of membrane and secondary bending stresses should not exceed 1.5 times the yield stress in order to prevent the collapse of the corrugations caused by pressure. Bellows subjected to external pressure can be analyzed in a manner similar to a cylinder, utilizing an equivalent moment of inertia. The fatigue life can be estimated based on the sum of deflections and pressure stresses as compared to S/N curves based on bellows test data or using the curves in B31.3 Appendix X, Metal Bellows Expansion Joints. Formulas for the stress analysis of bellows are available in the Expansion Joints Manufacturing Association (EJMA) Standards (37). 

Figure 12.17 Typical Wohler or "S-N" curve for polymers (stress amplitude

Figure 6.45 Fatigue life data, S-N curves, for a high-strength steel under different environmental conditions. Stress ratio R — — 7. Loading frequency 7 Hz for tests in 0.6 M NaCIsolution. Horizontal arrows indicate failure condition not attained. OCP = open-circuit potential102...

In considering fatigue, strength-based approaches use so-called S-N curves,... 

The influence of frequency on the S-N curve is shown for HIPS in Fig. 18. The general form of the S-N curve appears to change little with change of frequency. The fatigue data indicate that for PS, on reducing frequency by two decades, the average lifetime to failure is reduced by about a decade while for HIPS, with the same reduction in frequency of two decades, average lifetime is reduced about a decade and a half... 

For a HIPS sample tested at a stress amplitude of 17.2 MPa and a frequency of 0.2 Hz, hysteresis loops taken at various cycles (Fig. 7) indicated that craze initiation was first observed for this sample after about 20 cycles, while 283 cycles were required to fracture. For similar fatigue tests carried out at the lower frequency of 0.02 Hz, the cycles to fracture were decreased (from 283 to 64) and loop asymmetry and craze formation began sooner, at about 1-2 cycles. The changes produced in hysteresis loops with cycling are shown in Fig. 19. With decrease of test frequency reduces, the entire S-N curve shifts to the left as shown by Fig. 18, and, because of the increased time for each cycle, fatigue induced craze initiation occurs earlier in the specimen lifetime. 

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