Stress amplitude tests

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. 

Constant deflection amplitude fatigue testing is probably the less demanding of the two techniques, because any decay in the modulus of elasticity of the material due to hysteretic heating would lead to lower material stress at the fixed maximum specimen deflection. In the constant load amplitude tests, maximum material stress is fixed, regardless of any decay in the modulus of elasticity of the material. 

The four variables in dynamic oscillatory tests are strain amplitude (or stress amplitude in the case of controlled stress dynamic rheometers), frequency, temperature and time (Gunasekaran and Ak, 2002). Dynamic oscillatory tests can thus take the form of a strain (or stress) amplitude sweep (frequency and temperature held constant), a frequency sweep (strain or stress amplitude and temperature held constant), a temperature sweep (strain or stress amplitude and frequency held constant), or a time sweep (strain or stress amplitude, temperature and frequency held constant). A strain or stress amplitude sweep is normally carried out first to determine the limit of linear viscoelastic behavior. In processing data from both static and dynamic tests it is always necessary to check that measurements were made in the linear region. This is done by calculating viscoelastic properties from the experimental data and determining whether or not they are independent of the magnitude of applied stresses and strains. 

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. 

In linear viscoelastic behavior the stress and strain both vary sinusoidally, although they may not be in phase with each other. Also, the stress amplitude is linearly proportional to the strain amplitude at given temperature and frequency. Then mechanical responses observed under different test conditions can be interrelated readily. The behavior of a material in one condition can be predicted from measurement made under different circumstances. 

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... 

Several methods, as described in the preceding section, have been used to acquire information relative to the onset of the initial localized plastic deformation under alternating loading. Figure 5 is a plot of reflected light intensity vs. cycles for a transparent PS sample tested at 21 Hz at a stress amplitude of 17.2 MPa The number of cycles, N., to initiate the craze, as determined from the first jump in intensity over background, is about 5,000 cycles and the cycles to fracture, N, is about 11,000. In later sections, the ratio of to Np which in this example is about 0.45, is shown to be a function of both stress amplitude and frequency. 

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... 

Fig. 7. Hysteresis loops for HIPS vs. number of cycles for specimen tested at a stress amplitude of 17.2 MPa and at 0.2 Hz...

Fig. 10. Cycles to craze initiation, N, and cycles to fracture, Nj, vs. stress amplitude for PS tested at 21 Hz...

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. 13a—c. Fatigue fracture surfaces of HIPS tested at a low stress amplitude of 10.3 MPa and at 0.2 Hz a Low magnification scan b Higher magnification near source c High magnification near transition region... 

Fig. 15. Effect of frequency on cycles to fracture for PS specimens tested at stress amplitudes of 17.2 MPa and 20.7 MPa...

Figure 15 shows how the average fatigue lifetime of PS depends on frequency for two different stress amplitudes. The variation appears to be a linear one on this log-log plot, with the number of cycles to fracture increasing with increase of frequency, and at essentially the same rate for both stress amplitudes. For the rubber modified HIPS the fatigue endurance is plotted as a function of frequency in Fig. 16. Here too the lifetime increases with increase of test frequency and again the variation is a linear one on a log-lot plot. The slope of these curves is also essentially independent of stress...

Fig. 17. Cycles to fracture vs. frequency for samples of PS and HIPS tested at a stress amplitude of S 7.2 MPa...

Fig. 18. Stress amplitude vs. cycles to fracture of HIPS specimens tested at 0.2 Hz and 21 Hz...

Hysteresis loop observations have been made for both PS and HIPS at two frequencies, viz. 0.2 Hz and 0.02 Hz and at a stress amplitude of 17.2 MPa. It was noted in Fig. 6 that, for PS tested at 0.2 Hz and at a stress amplitude of 24.1 MPa there was no detectable change in loop area and hence no indication of appreciable crazing up to 1,450 cycles, the last cycle before fracture. Additional tests made at 0.02 Hz and 17.2 MPa show a similar behavior. For one sample that fractured at 803 cycles, loops were monitored for 660 cycles and no indication of plastic deformation was detected. 

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. 

For the rubber modified copolymer, ABS, we have carried out fatigue studies over a range of stress amplitudes and frequencies under reversed tension-compression cycling in addition, some tests have been made under cycUc tension. Results will be presented first for tests carried out under different applied amplitudes and comparisons will be made between ABS and SAN, between ABS and HIPS, and between our data on ABS and that of others... 

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