Variable amplitude loading

For constant amplitude loading, the basic SN-curve can be used with any surface roughness or mean stress corrections taken into account. For constant amplitude stress levels below the endurance limit of the material, the specimen or component will last for an essentially infinite number of cycles.

However, for variable amplitude loading with some loads above the endurance limit, even cycles with stress amplitudes below the endurance limit may affect the fatigue life. These effects are accounted for by using modified Miner rules. There are several modifications to the original Miner’s rule available in Specialist Durability:

• Elementary

• Haibach

• Liu-Zenner

• Hück-Pöting

The elementary and Haibach modifications only modify the SN-curve below the endurance limit, as illustrated in the figure below. The elementary Miner’s rule extends the SN-curve to approach zero stress amplitude using the same slope that the SN-curve has just above the endurance limit. In the figure, the original downward slope is denoted k.

The Haibach modification extends the SN-curve below the endurance limit with a slope of 2k-1, where k is the slope of the SN-curve just above the endurance limit. The curve is extended to approach zero stress amplitude. For several materials, modifications to the formula have been suggested in literature. Therefore, in Specialist Durability, you can also modify the Haibach-Miner rule by changing the constant.

The modification by Liu and Zenner adjusts the SN-curve to a crack propagation SN-curve. In the original SN-curve, the point that corresponds to the maximum load amplitude in the actual load is searched. The slope at this point is averaged with the slope of a typical crack propagation SN-curve. (In Specialist Durability, this slope is assumed to be 3.6.) The new endurance limit is set to half of its original value.

The modification by Hück suggests a variable slope of a reference SN-curve for the damage accumulation. A parameter C and the relation between the maximum stress value of the load spectrum distribution and the fatigue limit determine the slope of the reference SN-curve.

Keep in mind that the change of the endurance limit is caused by some damage in the structure and therefore by default it is modified only if the maximum load amplitude of the variable amplitude loading lies above the original endurance limit.

Note:

In Specialist Durability, you can also enforce the use of the modified SN-curve in the case only loads below the original endurance limit are applied.

Elementary Miner's Rule

Learn more

Defining SN-curves

Logarithmic nature of fatigue

Determination of SN-curves

How does the SN-curve definition via universal slope work?

Modifying factors of the SN-curve

Mean stress effects

Stress-life analysis in Specialist Durability

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Variable amplitude loading, Simcenter 3D 2021.1 Series

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