Solving Fatigue with Mean Stress

This video provides a comprehensive, 9-step methodology for solving fatigue problems involving mean stress (σm). When a component experiences both an alternating stress (σa}) and a non-zero mean stress, the analysis becomes more complex than fully reversed loading. This guide is essential for accurately assessing the lifespan of components in real-world applications like shafts, axles, and brackets.
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What You'll Master in 9 Steps:
1. Find the Rotating Beam Endurance Limit (S’e): Establish the baseline fatigue strength under ideal, fully reversed conditions.
2. Find the Actual Endurance Limit (Se) : Apply endurance limit modifiers (surface finish, size, etc.) to account for manufacturing and operating conditions, giving the material's actual infinite life limit.
3. Handle Notches/Stress Risers: If applicable, determine the fatigue stress concentration factor (Kf), which is crucial for accurately determining localized stress.
4. Apply Kf to Fatigue Stresses: Correct the calculated nominal alternating and mean stresses (σa & σm). using the stress concentration factor.
5. Check for Yielding: An essential static check to ensure the maximum stress (σmax = σa + |σm|) does not exceed the material's yield strength (Sy), which would cause permanent plastic deformation.
6. Check for Infinite Life: Determine if the stress state falls below the Modified Goodman Line or other relevant failure criteria to confirm if the component has an infinite lifespan.
7. Find the Equivalent Fully Reversed Stress Amplitude (σar): Use a mean stress correction criterion (e.g., Goodman, Soderberg, or Gerber) to convert the combined (σa & σm) stress state into a single, equivalent fully reversed stress (σar).
8. Find the Basquin Constants (a and b): Calculate the constants needed to define the high-cycle region of the S-N curve.
9. Solve for the Cycles to Failure (Nf): Use the Basquin relationship and the equivalent stress (σar) to predict the component's fatigue life. Apply safety factors if given.