CYCLIC LOADING and FAILURE 4/12/2018 4/12/2018 CYCLIC LOADING and FAILURE © 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION. 1

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

High-cycle fatigue loading is the most significant 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

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

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)

Coffin’s Law Basquin’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

Miner’s Rule of cumulative damage 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

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

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

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

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.