Library / Mechanical / MEC-89
Mechanical
Stress ratio of a fatigue cycle
Ratio of the minimum to the maximum stress.
- Ref
- MEC-89
- Rev
- v1
- Field
- Mechanical
- Result
- R
The stress ratio R = σmin/σmax describes the shape of a cycle: R = −1 for fully reversed, R = 0 for a zero-to-maximum cycle, and R close to 1 for a nearly steady load with a small ripple. Fatigue data and S–N curves are quoted for particular R values. It is undefined when σmax = 0.
Ratio of the minimum to the maximum stress. R = −1 is fully reversed loading, R = 0 is repeated tension from zero, and R is undefined when the maximum stress is zero.
Calculator
- Amplitude ratio, (1 − R)/(1 + R)2
- Stress amplitude80 MPa
- Mean stress40 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.
- With σmin = −40 MPa and σmax = 120 MPa, R = −0.3333: a cycle that dips into compression but is tensile on average, with an amplitude equal to 2 times the mean.
- R = −1 is the usual test condition (rotating bending), so data for other R values must be corrected for the mean stress.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| σmin Minimum stress in the cycle | −400 to 600 MPa | −3.333 | 5 | 8.333 | +20 MPa | −50 % |
| σmax Maximum stress in the cycle (nonzero) | −400 to 600 MPa | −1.2 | 1.2 | 2.4 | +20 MPa | −14.3 % |
Sweep of Minimum stress in the cycle
| Minimum stress in the cycle (MPa) | Stress ratio |
|---|---|
| −400 | −3.333 |
| −275 | −2.292 |
| −150 | −1.25 |
| −25 | −0.2083 |
| 100 | 0.8333 |
| 225 | 1.875 |
| 350 | 2.917 |
| 475 | 3.958 |
| 600 | 5 |
Sweep one variable
Variables and how each one contributes
Stress ratio
What the equation gives you. Everything else feeds it.
Maximum stress in the cycle (nonzero)
The maximum stress of the cycle, in MPa (tension positive). Raises R toward zero when σmin is negative (R is negative here, so a rise means a smaller magnitude): a larger maximum gives a smaller ratio magnitude. Raising it by 10 MPa (to 130 MPa) moves the result by −7.69 %, from −0.3333 to −0.3077.
Minimum stress in the cycle
The minimum stress of the cycle, in MPa (compression negative). Raises R, moving it towards 0 and then positive (R is negative here, so a rise means a smaller magnitude). Raising it by 10 MPa (to −30 MPa) moves the result by −25 %, from −0.3333 to −0.25.
Worked example with the values above
- Divide minimum by maximum: −40 / 120.
- R = −0.3333.
- So the cycle is tension–compression with a tensile mean (R = −0.3333).
Assumptions and limits
- A constant-amplitude cycle with nominally constant mean stress; stresses are the nominal local stresses.
- Tension is positive and compression negative, with σmax the algebraically larger value.
Common mistakes
- Using R when σmax is compressive: the definition then needs care, using the largest absolute stress.
- Mixing up R with the amplitude ratio.
Statistics and uncertainty
R is a ratio, so it is most sensitive to errors when σmax is small. For a cycle near zero-to-maximum, a small error in σmin moves R only a little but changes the damage noticeably.
Where it is used
- Matching a load cycle to the fatigue data available.
- Describing cycle shape in a design report or standard.
Maths you need
- Stress cycle: the repeated rise and fall of stress
- Tension positive: compression is entered as a negative stress