CYCLIC LOADING and FAILURE

1. CYCLIC LOADING and FAILURE

2. Loading and unloading a part is never completely reversible – energy is always lost – this fact is pronounced when loading is vibrational in nature • Damping coefficient η • Measure the degree to which a material dissipates vibrational energy • Loss coefficient η • Fraction of the stored elastic energy not returned on unloading

3. Low amplitude acoustic vibration High-cycle fatigue: cycling below the yield strength Low-cycle fatigue: cycling above the yield strength but below the tensile strength High-cycle fatigue loading is the most significant in engineering terms

4. Fatigue failures occur due to cyclic loading at stresses below a material’s yield strength • Depends on the amplitude of the stress and the number of cycles • Loading cycles can be in the millions for an aircraft • Fatigue testing must employ millions of fatigue cycles to provide meaningful design data

5. Fatigue characteristics are measured and plotted on an S-N curve • Stress amplitude • Mean stress • R value of -1 indicates the mean stress is zero • Endurance limit σe • Stress amplitude below which fracture does not occur at all or only after a very large number of cycles (>107)

6. Coffin’s Law • For low-cycle fatigue • Basquin’s Law • For high-cycle fatigue • The laws describe the fatigue failure of uncracked components cycled at a constant amplitude about a mean stress of zero

7. Goodman’s Rule • The corrected stress range can be plugged into Basquin’s law • Miner’s Rule of cumulative damage • When the cyclic stress amplitude changes, the life is calculated using Miner’s rule

8. Fatigue crack growth is studied by cyclically loading specimens containing a sharp crack • Cyclic stress intensity range • The range ΔK increases with time under constant cyclic stress because the crack grows in length

9. Safe design requires calculating the number of loading cycles possible before the crack grows to a dangerous length

10. Endurance limit is the most important property characterizing fatigue strength Metals/Polymers Glasses/Ceramics

11. SUMMARY • Static structures stand for a very long time • Eiffel tower • Golden Gate Bridge • Moving structures don't last as long • Materials can support static loads much better than changing loads • Metals: endurance limit is ONE THIRD of tensile strength • Materials are very sensitive to cyclic loads • Cracks are almost invisible until final failure occurs without warning • Surface treatment to reduce surface crack formation are now standard practice.