Fatigue life criteria

The fatigue life criteria equations define S-N or E-N curves using durability material properties.

S-N and E-N curves

In the S-N and E-N curves:

• S is the amplitude or the range of a stress cycle.

• E is the amplitude or the range of a strain cycle.

• N is the number of cycles or the number of reversals of stress or strain to failure.

S-N curve for brittle aluminium with a ultimate tensile stress of 320 MPa: stress in MPa vs life cycles

The S-N and E-N curves may also include the effect of mean stress of the loading cycle. Using the rainflow counting NOTE, the durability solver identifies the stress or strain amplitude and the mean stress of each cycle in the stress or strain time history of a transient event. The damage of each cycle is then evaluated using the S-N or E-N curve of the selected life criterion.

Life criteria, mean stress effects, plate thickness correction, and notch factor

The following table summarizes the characteristics of the available fatigue life criteria.

Fatigue life criteria	Fatigue evaluation	Fatigue application	Mean stress effect	Plate thickness correction	Notch factor	Material type
Smith-Watson-Topper	Strain-based	Low cycle	Included	Not applicable	Optional	Isotropic
Strain Life Maximum Principal	Strain-based	Low cycle	Optional	Not applicable	Optional	Isotropic
Strain Life Maximum Shear	Strain-based	Low cycle	Not applicable	Not applicable	Optional	Isotropic
Stress Life	Stress-based	High cycle	Optional	Optional	Optional	Isotropic
BWI	Stress-based	Low cycleHigh cycle	Optional	Optional	Not applicable	Isotropic
TWI	Stress-based	Low cycleHigh cycle	Optional	Optional	Not applicable	Isotropic
User-defined S-N curve	Stress-based	Low cycleHigh cycle	Optional	Optional	Optional	IsotropicOrthotropic
User-defined E-N curve	Strain-based	Low cycleHigh cycle	Not applicable	Not applicable	Optional	Isotropic
Hill	Stress-based	Low cycleHigh cycle	Optional	Not applicable	Not applicable	Orthotropic
Tsai-Wu	Stress-based	Low cycleHigh cycle	Optional	Not applicable	Not applicable	Orthotropic
Maximum Stress	Stress-based	Low cycleHigh cycle	Optional	Not applicable	Not applicable	Orthotropic

Note:

• High cycle fatigue requires more than 105 cycles to failure and is generally used for applications with low loads and relatively long lives. If the strength evaluation shows large margins of safety or safety factors, then high cycle fatigue is the likely failure mechanism.

• Low cycle fatigue requires a range of 10 – 105 cycles to failure and is generally used for applications with large loads and relatively short lives. If your strength evaluation shows small strength margins of safety or safety factors, the structure may not tolerate many cycles until failure, and low cycle fatigue is the likely failure mechanism.

In general, you should use strain history for strain-based fatigue evaluation and stress history for stress-based fatigue evaluation. See Understanding cyclic stress-strain behavior for information on how the durability solver converts amplitudes of strain cycles to and from amplitudes of stress cycles.

Using user-defined S-N and E-N curves

To use a user-defined S-N or E-N curve as the fatigue life criterion for computing durability results, you need to follow a workflow.

• Define the S-N or E-N curve for the material. The S-N curve has the number of cycles, N, also called duty cycles, as the independent variable, and stress amplitude, S, as the dependent variable. The E-N curve has the number of cycles, N, as the independent variable, and strain amplitude, E, as the dependent variable.

• Create a fatigue durability object.If you defined an S-N curve for isotropic materials, select Stress Life from the Fatigue Life Criterion list.If you defined an S-N curve for orthotropic materials, select the Perform Material Fatigue check box.If you defined an E-N curve, select either Strain Life Maximum Principal or Strain Life Maximum Shear from the Fatigue Life Criterion list.

• Use the fatigue durability object in your static or transient event and solve the durability event.

Learn more

Static events

Transient events

Durability damage evaluation

Durability objects

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Smith-Watson-Topper

Strain life

Stress life

BWI fatigue life criterion

TWI fatigue life criterion

User-defined S-N curve

User-defined E-N curve

Orthotropic material fatigue analysis

Plate thickness correction

Material properties for durability analysis

Understanding cyclic stress-strain behavior

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Fatigue life criteria, Simcenter 3D 2021.1 Series

© 2020 Siemens

Matsuishi, M., and Endo, T., “Fatigue of Metals Subjected to Varying Stress”, Japan Society of Mechanical Engineers, March, 1968.

Endo, T., et. al., “Damage Evaluation of Metals for Random or Varying Loading”, Proceedings of the 1974 Symposium on Mechanical Behavior of Materials, Volume 1, Society of Materials Science, Japan, 1974. pp. 371-380.

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