Learn: Fatigue stress ratio
Fatigue stress ratio R compares the minimum stress in a cycle with its maximum stress. It describes the cycle’s mean-stress character and is not a stress range or a resistance utilization ratio.
What the formula is saying
Divide signed σmin by signed σmax. A fully reversed cycle from −100 to +100 MPa gives R = −1; a zero-to-tension cycle gives R = 0.
Read the symbols in plain language
- σmin
- Minimum stress
Signed extreme stress in the same loading cycle; use the same tension/compression convention for both values.
MPaOne megapascal equals one N/mm² and 1000 kPa.
- σmax
- Maximum stress
Signed extreme stress in the same loading cycle; use the same tension/compression convention for both values.
MPaOne megapascal equals one N/mm² and 1000 kPa.
- R
- Result to find
Fatigue stress ratio. The same stress units cancel, and the sign carries information about reversal during the cycle.
ratio / no unit
Sort out the units first
Use matching stress units, here MPa, so they cancel. R is dimensionless and may be negative. Maximum stress must be nonzero for this ratio to be defined.
Assumptions before calculating
Assume both extremes belong to the same cycle, point and stress component, with tension positive and compression negative. Require σmax ≥ σmin but do not force all valid ratios into the interval 0–1.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
Read the supplied values as one complete study case. Find R and explain the result in the stated output unit.
- σmin · Minimum stress
- 50 MPa
- σmax · Maximum stress
- 200 MPa
Retain the signed minimum stress
A compressive minimum remains negative under the chosen tension-positive convention.
(50) = 50 MPaDivide by the nonzero algebraic maximum
The same stress units cancel, and the sign carries information about reversal during the cycle.
(50) ÷ (200) = 0.25
Does this worked answer make sense?
Equal nonzero extrema give R = 1 and zero stress range. Scaling both extrema by the same positive factor leaves R unchanged.
A second worked example — different values
A second case uses different data. Predict which way the answer will change, then calculate it without reusing the first answer.
- σmin · Minimum stress
- -100 MPa
- σmax · Maximum stress
- 100 MPa
Retain the signed minimum stress
A compressive minimum remains negative under the chosen tension-positive convention.
(-100) = -100 MPaDivide by the nonzero algebraic maximum
The same stress units cancel, and the sign carries information about reversal during the cycle.
(-100) ÷ (100) = -1
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Solve this separate case yourself. Use only the values below; the two worked examples use different data. Give the requested result in the selected unit.
- σmin · Minimum stress
- -40 MPa
- σmax · Maximum stress
- 160 MPa
Find: Learn: Fatigue stress ratio
A hint, not the answer
Divide signed σmin by signed σmax. A fully reversed cycle from −100 to +100 MPa gives R = −1; a zero-to-tension cycle gives R = 0.
Use matching stress units, here MPa, so they cancel. R is dimensionless and may be negative. Maximum stress must be nonzero for this ratio to be defined.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Retain the signed minimum stress
A compressive minimum remains negative under the chosen tension-positive convention.
(-40) = -40 MPaDivide by the nonzero algebraic maximum
The same stress units cancel, and the sign carries information about reversal during the cycle.
(-40) ÷ (160) = -0.25
Avoid the common trap
Do not divide the stress range by maximum stress, use magnitudes instead of signs, or divide by zero when the maximum equals zero. Negative R is meaningful rather than automatically an error.
When this method applies — and when it does not
A wholly compressive cycle can produce R > 1 under this algebraic convention because both stresses are negative. The ratio does not establish a fatigue strength reduction; use a material-appropriate mean-stress or fatigue procedure.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Reading focus: Fatigue stress ratio. Stress cycles, ranges and life under repeated loading. Linear cumulative damage is an idealization and does not account for load-sequence effects.
Lesson updated: · Both examples and the separate practice case are checked against an independent high-precision numerical implementation. This verifies arithmetic for the stated model, not engineering certification.