e-N curve

In: Theory basis

The label e-N curve is used throughout this Help, since the common label Manson-Coffin curve is not quite precise. The Manson-Coffin formula desribes only the dependency of plastic strain εp on the number of cycles N:

The complete e-N curve relates to the relation between total strain and the number of cycles. The elastic part of strain εe, which can be readily  related to stress via Hooke's law, has to be thus retrieved via Basquin formula:

The complete e-N curve thus can be described by the sum of two previous terms:

Unlike the S-N curve, this is used as a purely material characteristics. The local strains are used there and thus no notch-like effects are involved.

Note: Well, I wonder why there are no variations in e-N curves for e.g. different surface roughnesses. The roughness is a micro-property, which cannot be reflected in any sound FE-model. Apparently, the fatigue factors similar to those applied onto the S-N curves should be applicable, but I have not heard about anything like this used. Can anybody help?

Note 2: The curve for the torsion loading can be described by a similar formula:

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Please, be aware that the exponents here differ from the exponents valid for tension. There are nevertheless authors who prefer to use the same coefficients for both load modes ([BS92]), because of the material parameters for the torsion mode are very rarely available. Currently, the same exponents are also used in PragTic.

The specific property of the e-N curve in comparison with the S-N curve is, that the final number of cycles N refers to the initiation of the crack of a technical size, and not to the final rupture of the specimen.

The common computational scheme of the use of the e-N curve is, that the stress cycle retrieved from the continuous load history by the rain-flow decomposition is input into second formula above and the corresponding number of cycles is computed. If the cycle has other mean value than zero a mean stress correction can be applied - see all the uniaxial local elastic-plastic strain methods. The number of cycles cannot be set explicitly from the final e-N formula, thus the Newton-Raphson iterative scheme is used in PragTic. The damage induced by one such a cycle is set to be a reciprocal value to the number of cycles. This partial damage is summed with the damages induced by other cycles in the load history by the Palmgren-Miner rule.

Material parameters

More:

S-N curve

Damage accumulation concept

rain-flow decomposition

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