There are no fixed rules. Your data should be statistically significant to construct the Basquin Power law. Since the fatigue data can be best represented by Weibull statistics, typically 6 specimens at every stress amplitude are required. If you plan, 6 stress amplitudes, it works out to ~36 specimens (something similar to the suggestion made by Igor above). Instead of concentrating on multiple tests (say 6) at each stress amplitude, I would rather prefer to stagger the stress amplitude (plan more stress amplitude levels) so that a neat spread of data can be obtained. The best way that I would follow is do minimum tests at high stress amplitudes (may be 3 each) and reduce the stress amplitude interval or increase the repeat tests at lower stress amplitude. The reason is normally scatter in the data will be low at high stress amplitudes and will be more as you go down. So either increase the number of tests or decrease the gap between the stress amplitude condition. Take your call. After all you have to perform an "acceptable" curve fitting to your data (may be with a R^2 of 0.999, if you plot the data in log-log scale).

It depends on the number of cycle range which you want to investigate . An other point is , if you want to have a stastically absolutely reliable result . For both LCF and HCF region you need aproximatley 6 points in a wide stress range

Dear Feng,

The nature of mechanical behavior of metallic materials is probabilistic. Confinement of any mechanical test with bare minimum of specimens reduces the confidence level in interpretation of test results. Scatter in high cycle fatigue test results is significantly large than any other mechanical test. The incremental research in this complex research field has now established that the scatter is linked to the material microstructure itself, if the test conditions are properly controlled. The intrinsic microstructural constituents (their orientation with respect to external loading direction etc. ) causing strain localization and eventually failure varies from specimen to specimen. You have to understand the microstructural constituents of the material first before deciding the number of specimens. If the weakest link for causing failure is more, one should opt for large number of specimens. It is not easy to pin down the total number of specimens for plotting S-N curve. However, as a crude approximation, one should always consider minimum 6-8 stress levels and minimum three specimens at each stress level. Remember, the material itself is the best guidespot to tell you the minimum number of specimens. All the best, 

You will get a good idea about the number of points in Fig. 3.1 of the attached document. It may be seen in this figure more points are required to define the shape of the S_N curve in steel which shows a definite endurance limit as compared to  aluminum alloy that does not show  endurance limit. In the case of the former, the safe stress to avoid fatigue failure is readily seen but in the latter case the safe stress is arbitrarily chosen at 10^7 cycles. However, the point at which S-N curve attains zero slope should be clearly known in the case of steel while only the trend of S-N curve is necessary for aluminum alloys. Thus it may be argued that steel requires many more data points than aluminum. This is indeed reflected in Fig.3.1. It is safer, however to have more data points for steel than for aluminum. 6 points may be sufficient for aluminum alloy but for steel at least 15 points will be needed to get usable S-N curves ( I presume that you need the answer for demonstration and not for design)   

Thanks for answering my question. 

But I have time constraint during my fatigue testing, That's why I make my run-out cycle at 1 million.

Hi,to design S-N curve, it will be enough to perform 10 tests to get 10 points on the graph

Dear prof Vladislav, 10 tests includes 3 times repeat or just 10 stress level?

 Hi,if you know the material ultim strenght, you should load rotating cpecimen by the load which generates in it approx 90 percent of ultim strength to determine the first number of cycles to failure. Second cpecimen you load by 80 perc and determine corresp number of cycles. 10 cpecimens is enough to determine lower part of S-N curve and draw the asymphtote to it, which indicates fatigue limit.

Thank you for your answer but is the result reliable since we don't do the 3 times repeat? 

There will be assessments you can do to tell how many specimens you might need to provide a statistical confidence but in practical terms you could perform 10 tests at 5 stress/strain levels to give you a good indication of the behaviour. More tests (e.g. 3 or more per stress/strain level) would then be required if you wanted a more robust statistical assessment.

recommend reading this for uncertainity sources,  Ihttp://www.npl.co.uk/upload/pdf/cop02.pdf

If the test uncertainties are not addressed properly it can easily bias the resulting LCF curve. Fitted curve will be somewhere in +/- 2 sigma band. With a minimal number of tests you are basically looking for a random curve that will stay in this +/- band.

Good day, is this Including 3 times repeat?

There are no fixed rules. Your data should be statistically significant to construct the Basquin Power law. Since the fatigue data can be best represented by Weibull statistics, typically 6 specimens at every stress amplitude are required. If you plan, 6 stress amplitudes, it works out to ~36 specimens (something similar to the suggestion made by Igor above). Instead of concentrating on multiple tests (say 6) at each stress amplitude, I would rather prefer to stagger the stress amplitude (plan more stress amplitude levels) so that a neat spread of data can be obtained. The best way that I would follow is do minimum tests at high stress amplitudes (may be 3 each) and reduce the stress amplitude interval or increase the repeat tests at lower stress amplitude. The reason is normally scatter in the data will be low at high stress amplitudes and will be more as you go down. So either increase the number of tests or decrease the gap between the stress amplitude condition. Take your call. After all you have to perform an "acceptable" curve fitting to your data (may be with a R^2 of 0.999, if you plot the data in log-log scale).