In fatigue analysis, satisfying 4 times (scatter factor 4) of the required life cycles has the 99% of the material reliability (probability) as far as I know.
For instance, if the requirement is 100,000 cycles and the analysis shows the life is more than 400,000 cycles, the material is expected to meet the requirement (100,000 cycles) with 99% reliability.
But, in my recent project, it required me to use scatter factor 4 and perform 4 life fatigue test.
In other words, if the requirement is 100,000 cycles as the above, the analysis should meet 400,000 cycles and its fatigue test should also succeed 400,000 cycles.
Here, I have a conflict. The analysis with scatter factor 4 can guarantee 100,000 cycles with 99% reliability. But after that amount of cycles, it cannot anymore. So, if the test fails between 2 and 4 life, there may be a material probability issue.
In order to guarantee the 4 life test, do I have to use scatter factor 16? It sounds too conservative. Its requirement cycles are 100,000 but the fatigue test should perform 4 lives.
What should I do to guarantee the fatigue requirement as performing the fatigue analysis?
To me, your analysis approach seems somehow too simplified and basically of a deterministic type. If the goal is to compute the failure probability, the information on the PDF must also be provided. Saying that a standard deviation of four gives a certain failure probability in not sufficient, unless the information on cycle PDF is given (or maybe is tacitly understood in your post).
Also the uncertainty of SN parameters estimated on fatigue data (i.e., statistical uncertainty) should be taken into account for a complete reliability analysis, for example by defining a characteristics SN curve for a certain failure probability or defining a confidence interval – maybe this is actually your goal. This task can be accomplished for example by considering a SN curve defined by tolerance interval.
Denis Benasciutti
Thanks for your answer. I think the question title looks confusing. Actually, it is not my goal to compute the probability. I do the analysis with a typical approach. I work with S-N curves from MMPDS, surface factor, load factor, temperature factor, reliability factor and so on.
From Shigley's Mechanical Engineering Design, 0.814 of the factor can be applied to the endurance limit and this means 99% reliability of the material. Instead of using the factor, applying Scatter factor 4 to the required cycle has similar reliability as far as I know and this approach is normally accepted in my field.
The reliability factor or scatter factor itself is not the problem. My question is about how to deal with the test requirement of 4 lives. For example, the actual required life is 100,000 cycles and it should be qualified with 4 times fatigue test (400,000). What is a real requirement to me for the fatigue analysis? 100,000 or 400,000?
If I consider 100,000 with the scatter factor or the reliability factor, I could be confident to the first life fatigue test and not for the rest of it.
If I consider 400,000 with those factors, it is so conservative.
This makes me confused.
I am not good at writing. I hope you to understand my point. :)
Thanks,
Be careful with the assumptions that are being made.
1) 0.814 assumes that the standard deviation of the Log(N) = 8%, which is not true for all metals. Shigley is pretty clear the he had data from a handful of alloys and that was the biggest standard deviation.
2) Testing to 4x life does not guarantee you have 99% reliability. But a 4x life test is a common requirement, especially in airframe design.
3) Don't try to make sense of the 4x and the 0.814 factor. They are unrelated rules of thumb. The material you are working with may or may not follow either of those rules.
4) The S-N curves in MMPDS include all the information you need to calculate a 99% probability of exceedance line. The method and an example are included in Section 9.6.1.11.
5) Many MMPDS curves are modeled assuming constant scatter.
Doug Hall
Thank you for your answer. Could you let me know the title of MMPDS Section 9.6.1.11 you mentioned? I have MMPDS-11 and cannot find the section. I think we have different version of MMPDS each other.
By the way, do you mean I could use those factors, 4x and 0.814 at same time for the analysis I am working on? Is it a common approach for 4x life test requirement?
In MMPDS-11 (which has been superseded), 9.6.1.11 Estimation of Lower Tolerance Bounds for Fatigue Data provides a method for estimating a lower bound with a specific probability of exceedance and confidence.
The 4x and 0.814 are different approaches to estimating a lower bound on the fatigue life. In Aerospace, there are applications where the 4x life test is required. But there are materials where the ratio between the first percentile and the typical life is more than 10x.
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