Why do ferrous and titanium alloys have a fatigue limit but others don't?
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Do you mean why do ferrous and titanium alloys have an endurance limit, i.e. if the stress doesn't exceed the endurance limit the fatigue life is effectively infinite?
The reason is that below the endurance stress level, some components of the alloy (e.g. carbon in steel alloys) prevent the dislocations from moving and therefore prevent micro-cracks from growing. If you exceed the endurance limit the dislocations can still move and the fatigue life is "used up"..
For alloys like magnesium and copper there is no corresponding structures in the alloys, so the material will eventually fail in fatigue however low the stress level is. Usually components in these materials are designed to a stress level that gives a fatigue life of 10^8 or more cycles.