Fatigue stress amplitude

The behaviour of steel under fatigue loading exhibits a property known as the fatigue limit. This is a value of the fatigue stress amplitude below which the fatigue life of the... 

Fig. 8.22. Modified Goodman diagram showing fatigue stress amplitude required to cause failure in 10 cycles as a function of mean stress for two carbon-fibre reinforced epoxy resin materials (a) unidirectionally reinforced, stressed parallel to fibres, and (b) cross-plied laminate, with 45% of plies parallel to stress, and 55% transverse. Fibre volume fraction 60% (after R. Tetlow).

SS Given a set of fatigue stress amplitude and cycles-to-faUure data, develop a spreadsheet that allows the user to generate an S -versus-log N plot. 

For convenience, in the previous sections it has been arranged so that the mean stress is zero. However, in many cases of practical interest the fluctuating stresses may be always in tension (or at least biased towards tension) so that the mean stress is not zero. The result is that the stress system is effectively a constant mean stress, a superimposed on a fluctuating stress a a- Since the plastic will creep under the action of the steady mean stress, this adds to the complexity because if the mean stress is large then a creep rupture failure may occur before any fatigue failure. The interaction of mean stress and stress amplitude is usually presented as a graph of as shown in Fig. 2.76. 

This represents the locus of all the combinations of Ca and Om which cause fatigue failure in a particular number of cycles, N. For plastics the picture is slightly different from that observed in metals. Over the region WX the behaviour is similar in that as the mean stress increases, the stress amplitude must be decreased to cause failure in the same number of cycles. Over the region YZ, however, the mean stress is so large that creep rupture failures are dominant. Point Z may be obtained from creep rupture data at a time equal to that necessary to give (V cycles at the test frequency. It should be realised that, depending on the level of mean stress, different phenomena may be the cause of failure. 

During fatigue the stress amplitude usually remains constant and brittle failure occurs as a result of crack growth from a sub-critical to a critical size. Clearly the rate at which these cracks grow is the determining factor in the life of the component. It has been shown quite conclusively for many polymeric materials that the rate at which cracks grow is related to the stress intensity factor by a relation of the form... 

Examples of fatigue curves for unreinforced (top) and reinforced (bottom) plastics are shown in Fig. 2-44. The values for stress amplitude and the number of load cycles to failure are plotted on a diagram with logarithmically divided abscissa and English or metrically divided ordinates. 

The analytical solutions derived in Sections 4.3 and 4.4 for the stress distributions in the monotonic fiber pull-out and fiber push-out loadings are further extended to cyclic loading (Zhou et al., 1993) and the progressive damage processes of the interface are characterized. It is assumed that the cyclic fatigue of uniform stress amplitude causes the frictional properties at the debonded interface to degrade... 

Figure 5.41 Stress amplitude versus cycles to failure illustrating (a) fatigue limit and (b) fatigue life. Reprinted, by permission, from W. Callister, Materials Science and Engineering An Introduction, 5th ed., p. 212. Copyright 2000 by John Wiley Sons, Inc.

FIG. 25.6 Stress amplitude vs. fatigue lifetime in number of stress cycles. 

It should be observed, that the comparison of the "fatigue strength" reduction is different for the probes stress amplitudes for the uniaxial, pressure amplitudes for the pipe specimen. 

As shown in Fig. 2, the variables describing a fatigue experiment are numerous. Besides mean stress, stress amplitude, and frequency, the load type and history have to be selected in a proper way prior to testing. 

Effects of Stress Amplitude and Stress State on Fatigue Behavior. . . 181... 

TensUe tests, at controlled strain rates, were performed on an Instron tensile tester. Samples were rectangular, 6.35 mm by 3.17 mm in cross-section, or cylindrical, with a diameter of 5.1 mm. Both types had a gauge length of 12.7 mm. Fatigue tests were carried out on similar cylindrical samples, or on rectangular specimens, 5.1 mm by 3.17 nun in cross-section, at various selected stress amplitudes and at frequencies... 

Fig. 4. Photograph of PS fatigue specimen cycled for 80% of its expected fatigue life at a stress amplitude of 17.2 MPa and at 21 Hz...

For non-transparent specimens, as shown by Bucknall and Stevens useful information relative to the deformation mode can be obtained by recording hysteresis loops as a function of cycles. Figure 6 shows hysteresis loops obtained at 0.2 Hz at various N values for PS tested at a stress amplitude of 24.1 MPa and Fig. 7 for HIPS tested at 17.2 MPa. For PS, with Nf = 1,451 cycles, there is no detectable change in loop area at this stress amplitude up to the final cycle. This illustrates the highly localized nature of the fatigue-induced damage zone in PS and indicates that, for this polymer, hysteresis loop observations are not an effective method for detecting craze... 

Figure 13 shows a typical fatigue fracture surface for a HIPS sample tested at 0.2 Hz at a low stress amplitude of 10.3 MPa. To note the effect of stress amplitude, these pictures should be compared with those of Fig. 9 obtained at a higher stress amplitude of 17.2 MPa. At the lower stress amplitude the fracture surface. Fig. 13 a, is markedly different from that of Fig. 9 a. Here fracture developed from a surface... 

Fig. 12 a and b. Fatigue fracture surfaces of PS tested at a stress amplitude of 24.1 MPa and at 0.2 Hz a Low magnification scan b High manification of region beyond DCG bands... 

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