What is Stress Ratio?
The stress ratio (R) is a fundamental parameter in fatigue analysis that characterizes the nature of cyclic loading. It is defined as the ratio of minimum stress to maximum stress during a loading cycle.
Understanding the stress ratio helps engineers predict fatigue life and select appropriate materials for components subjected to cyclic loads.
How to Calculate Stress Ratio
The formula for stress ratio is:
[R = \frac{\sigma_{\min}}{\sigma_{\max}}]
Where:
- ฯ_min is the minimum stress in the loading cycle
- ฯ_max is the maximum stress in the loading cycle
- Tension is positive, compression is negative
Common Stress Ratio Values
| R Value | Loading Type | Description |
|---|---|---|
| R = -1 | Fully reversed | Equal tension and compression |
| R = 0 | Zero-to-tension | Pulsating from zero to max |
| R = 0.1 | Tension-tension | Common test standard |
| R = 1 | Static | No cycling (constant load) |
| R < 0 | Partially reversed | Some compression in cycle |
Calculation Examples
Fully Reversed Loading (R = -1)
A shaft experiences stress cycling between +100 MPa (tension) and -100 MPa (compression):
[R = \frac{-100}{100} = -1]
This is the most damaging type of fatigue loading.
Zero-to-Tension Loading (R = 0)
A bolt is tightened and then loaded, cycling between 0 and 200 MPa:
[R = \frac{0}{200} = 0]
This is a pulsating load condition.
Tension-Tension Loading (R = 0.5)
A component cycles between 50 MPa and 100 MPa:
[R = \frac{50}{100} = 0.5]
The material never experiences compression.
Related Parameters
Mean Stress
[\sigma_m = \frac{\sigma_{\max} + \sigma_{\min}}{2}]
Stress Amplitude
[\sigma_a = \frac{\sigma_{\max} - \sigma_{\min}}{2}]
Stress Range
[\Delta\sigma = \sigma_{\max} - \sigma_{\min}]
Why Stress Ratio Matters
Fatigue Life Prediction
S-N curves (stress-life curves) are typically generated at specific R values. Converting between R values requires correction factors.
Material Selection
Some materials are more sensitive to mean stress effects than others. Understanding R helps in material selection.
Design Optimization
Knowing the expected stress ratio helps engineers design for the appropriate fatigue conditions.
Testing Standards
Most fatigue testing is done at R = 0.1 for tension-tension or R = -1 for fully reversed loading, providing baseline data for comparison.