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I'm designing a shaft, and i have to choose a material.
I deal with cyclic stress in my machine, so i set up an expression for all the possible stresses and combined it with von Mises criteria for plastic deformation, it gives me the so called comparison stress.
This comparison stress should be lower than the endurance limit of the material. I don't have the endurance limit, but instead the tensile strength. Is there any connection between endurance limit and the tensile strength ?
Yes, to a degree.
The endurance limit is normally expressed as a fraction of the yield stress and for steel a typical value is 1/2 (50%). This is is certainly a reasonable assumption for common low alloy, medium carbon steels ie the sort of steels that you might reasonably select for a shaft.
In fact for many practical purposes the factor of safety that you use to account for dynamic loading will be similar or greater than this anyway so it's often not a limiting factor in steel.
Equally for high performance, highly optimised designs you might not consider endurance stress as an absolute limitation and just design the part with a fatigue life.
And for really critical parts you relay need to consider the very detailed design in terms of surface finish, surface treatments and manufacturing processes as well as things like minimum radii when calculating fatigue life, for which tables of coefficients exist.
In general in engineering design optimisation is a process of getting increasingly confident about the actual real world loads a part will see, a process which is very much subject to diminishing returns and for general purpose deign it is often a case of selecting a sensible and pragmatic factor of safety in which you can be confident.
Response to comment by OP
It is mostly empirical. The difficulty with fatigue is that it is highly dependant on local stress raisers. As a bulk material steel is not very susceptible to fatigue, but you can easily get local stress concentrations eg around a surface defect in the wrong place which exceed the yield stress of the material and consequent work hardening over multiple cycles.
This isn't exactly the same mechanism as fatigue in say aluminium which has a very low endurance limit, even in ideal conditions.
As with many things in practical engineering it boils down to an empirical coefficient whcih is known to work for a given context.
per wikipedia:
Typical values of the limit for steels are 1/2 the ultimate tensile strength, to a maximum of 290 MPa
https://en.wikipedia.org/wiki/Fatigue_limit
Whether you want to rely on such a rule of thumb depends on your application.
I suspect not, based on a table provided here . It would appear that the relationship is strongly material-dependent and not analytically calculable.
Steels are relatively unique among metals with a very reliable endurance limit equal to 1/2 of tensile strength. Cast irons definitely do not have this feature. Nickel and cobalt alloys might have it but there is limited data. Fatigue test coupons are smooth with no stress concentration ; not to say that they never contain an inclusion. So fatigue tests give the best possible value; Real world components normally have various stress concentrators. It is the duty of the builder to determine the severity of these stress concentrators. By "endurance limit" I mean the number of stress cycles approach infinity.
