Library / Mechanical / MEC-90
Mechanical
Modified Goodman factor of safety
Fatigue factor of safety for a high-cycle uniaxial load when the alternating and mean stresses are scaled up in proportion.
- Ref
- MEC-90
- Rev
- v1
- Field
- Mechanical
- Result
- n
The modified Goodman line combines fatigue amplitude and mean stress into one safety margin: 1/n = σa/Se + σm/Sut, where Se is the endurance limit of the actual part (already reduced for size, surface and so on) and Sut is the ultimate tensile strength. It gives a factor of safety n for infinite life. It is a straight line between Se on the amplitude axis and Sut on the mean-stress axis, and a stress state on the line has n = 1. It is conservative; the yield limit should also be checked separately.
Fatigue factor of safety for a high-cycle uniaxial load when the alternating and mean stresses are scaled up in proportion. It is an empirical screening relation and does not replace a yield check.
Calculator
- Damage index, σa/Se + σm/Sut0.6
- Largest amplitude allowed at this mean stress144 MPa
- Factor on the amplitude alone, at the same mean1.8
- Largest mean stress allowed at this amplitude200 MPa
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- For an amplitude of 80 MPa, a mean of 40 MPa, Se = 160 MPa and Sut = 400 MPa the factor of safety is 1.67. The amplitude takes 83.3 % of the margin and the mean stress the rest.
- The amplitude is allowed to rise by a factor of 1.8 before the line is reached; because n measures both together, this is not the same as n.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| σa Stress amplitude | 1 to 500 MPa | 0.3101 | 9.412 | 9.102 | +10% | −7.69 % |
| Se Corrected endurance strength | 20 to 800 MPa | 0.2439 | 5 | 4.756 | +10% | +8.2 % |
| σm Mean stress (not compressive) | 0 to 500 MPa | 0.5714 | 2 | 1.429 | +10% | −1.64 % |
| Sut Ultimate tensile strength | 100 to 2,000 MPa | 1.111 | 1.923 | 0.812 | +10% | +1.54 % |
Sweep of Stress amplitude
| Stress amplitude (MPa) | Fatigue factor of safety |
|---|---|
| 1 | 9.412 |
| 63.38 | 2.016 |
| 125.8 | 1.129 |
| 188.1 | 0.7838 |
| 250.5 | 0.6004 |
| 312.9 | 0.4865 |
| 375.3 | 0.4089 |
| 437.6 | 0.3527 |
| 500 | 0.3101 |
Sweep one variable
Variables and how each one contributes
Fatigue factor of safety
What the equation gives you. Everything else feeds it.
Stress amplitude
The stress amplitude of the cycle, in MPa. Lowers the factor of safety: a larger amplitude uses up more of the fatigue strength. Raising it by 10 MPa (to 90 MPa) moves the result by −9.43 %, from 1.667 to 1.509.
Mean stress (not compressive)
The mean stress of the cycle, in MPa (tensile positive). Lowers the factor of safety, though less than the amplitude because Sut is larger than Se. Raising it by 10 MPa (to 50 MPa) moves the result by −4 %, from 1.667 to 1.6.
Corrected endurance strength
The endurance limit of the part, in MPa, after correction for size, surface finish and loading. Raises the factor of safety: a higher endurance limit tolerates a larger amplitude. Raising it by 10 MPa (to 170 MPa) moves the result by +5.15 %, from 1.667 to 1.753.
Ultimate tensile strength
The ultimate tensile strength of the material, in MPa. Raises the factor of safety, but only slightly while the amplitude term dominates. Raising it by 20 MPa (to 420 MPa) moves the result by +0.8 %, from 1.667 to 1.68.
Worked example with the values above
- Amplitude term: σa/Se = 80 / 160 = 0.5.
- Mean term: σm/Sut = 40 / 400 = 0.1; sum = 0.6.
- n = 1 / 0.6 = 1.667.
Assumptions and limits
- A constant-amplitude cycle with constant mean stress, in a material that has an endurance limit (steel, for example).
- Both Se and Sut are for the actual part, and the mean stress is tensile; for a compressive mean stress the Goodman line is usually taken as flat, with σm treated as 0, as that is the safe assumption.
Common mistakes
- Using the specimen endurance limit without correcting for size, surface and loading.
- Forgetting to check the yield (Langer) line for the peak stress.
- Using the formula for aluminium, which has no true endurance limit.
Statistics and uncertainty
Fatigue data scatter widely, so Se is the uncertain input. A factor of safety of 1.5 to 2 is common in practice because the endurance limit has a scatter of 10 to 15 % and is lowered by size, surface and environment. The factor relates to infinite life only, and does not give a life estimate.
Where it is used
- The safety margin for a shaft, spring, connecting rod or bolted joint under varying load.
- Comparing design options for infinite fatigue life.
Maths you need
- Stress cycle: the repeated rise and fall of stress
- Tension positive: compression is entered as a negative stress
- Endurance limit: the stress amplitude that can be applied for an unlimited number of cycles