JLBK56
Mechanical
- Jun 12, 2022
- 5
Hi all. I've noticed an inconsistency in the Goodman equivalent stress as presented in Shigley's (10e) and was wondering if anyone could help me out in understanding it. The tenth edition of Shigley's provides an example (Example 6-12) for determining the Goodman equivalent stress for non-zero mean stress fatigue. In this example, the book solves for the fatigue factor of safety for infinite life as as n[sub]f[/sub] = 1/(s[sub]a[/sub]/S[sub]e[/sub] + s[sub]m[/sub]/S[sub]ut[/sub]) where s[sub]a,m[/sub] are the mean and alternating stress components, S[sub]e[/sub] is the material's endurance limit, and S[sub]ut[/sub] is the material's ultimate strength. Given an alternating stress of 40 ksi, a mean stress of 20 ksi, an endurance limit of 40 ksi, and an ultimate strength of 80 ksi, the factor of safety against infinite life turns out to be 0.8, indicating that infinite life isn't expected.
The equivalent stress is (conceptually) defined such that it is the completely reversed stress that causes identical damage to the part, and is calculated by replacing S[sub]e[/sub] with s[sub]rev[/sub], and can be rearranged to show s[sub]rev[/sub] = s[sub]a[/sub]/(1-s[sub]m[/sub]/S[sub]ut[/sub]) = 53.3 ksi.
Here comes the discrepancy: Calculating the fatigue factor of safety using this equivalent completely reversed stress would result in n[sub]f[/sub] = S[sub]e[/sub]/s[sub]rev[/sub] = 0.75, which is different from the fatigue factor of safety calculated above. Can anyone explain this paradox? Perhaps it isn't necessarily inconsistent, and I'm incorrectly interpreting the fatigue factor of safety. Any thoughts would be well appreciated.
On a side note - I know that the recommendation provided in this forum is to use the maximum principal stress for fatigue calculations, however I noticed that Shigley's has a section dedicated to the use of von-Mises stress for generalized loading in fatigue. Does anyone have any thoughts related to this, and why there's a discrepancy between Shigley's and recommendations by this community?
Thanks!
The equivalent stress is (conceptually) defined such that it is the completely reversed stress that causes identical damage to the part, and is calculated by replacing S[sub]e[/sub] with s[sub]rev[/sub], and can be rearranged to show s[sub]rev[/sub] = s[sub]a[/sub]/(1-s[sub]m[/sub]/S[sub]ut[/sub]) = 53.3 ksi.
Here comes the discrepancy: Calculating the fatigue factor of safety using this equivalent completely reversed stress would result in n[sub]f[/sub] = S[sub]e[/sub]/s[sub]rev[/sub] = 0.75, which is different from the fatigue factor of safety calculated above. Can anyone explain this paradox? Perhaps it isn't necessarily inconsistent, and I'm incorrectly interpreting the fatigue factor of safety. Any thoughts would be well appreciated.
On a side note - I know that the recommendation provided in this forum is to use the maximum principal stress for fatigue calculations, however I noticed that Shigley's has a section dedicated to the use of von-Mises stress for generalized loading in fatigue. Does anyone have any thoughts related to this, and why there's a discrepancy between Shigley's and recommendations by this community?
Thanks!
