Defining SN-curves

The SN-curves for ferrous alloys can be composed of a series of straight-line segments on the log-log diagram. At high load levels, static failure due to the ultimate stress of the material (Smax) may be reached, and is represented by the initial horizontal segment. At the stress level just below Smax, the specimen may last a relatively small number of cycles, and this corresponds to N0 on the diagram. At lower stress amplitudes, the specimens last longer, and this is represented by one or two sloped segments of the SN-curve, defined by the points S1 − N1 and SE − NE, or by the slopes of the lines and the starting points. The last segment of the SN diagram is again horizontal, and indicates that at any stress amplitude at or below the endurance limit (SE) that no fatigue failure is likely to occur.

Representation of the SN-Curve

Parameter	Meaning	Unit
NE	No of Cycles at endurance limit	1
SE	Load Amplitude value at endurance limit	MPa, N, Nm
N1	No of Cycles at the intermediate point. (Set to NE if there is only one slope)	1
S1	Load Amplitude at the intermediate point. (Set to SE if there is only one slope)	MPa, N, Nm
k1	Inverse slope of the lower segment	1
k2	Inverse slope of the upper segment	1
Smax	Tensile Strength	MPa, N, Nm
SMIN	Compressive Strength	MPa, N, Nm

Constant amplitude SN-curves for non-ferrous alloys such as aluminum alloys typically do not exhibit an endurance limit, although a pseudo endurance limit is often used. A pseudo endurance limit is stress amplitude value that corresponds to a number of cycles that is larger than expected to result from the fatigue analysis.

In either case, the SN-curve can be defined in Specialist Durability by specifying a point field or a slope field. In addition to the tensile strength, the compressive strength can be defined in the Simcenter 3D material data. These strength values are used to determine if a static (overload) failure has occurred. If the largest tensile load in a time history is above the tensile strength, or the largest compressive load magnitude is above the compressive strength, then a static failure mode is reported.

Although the SN-curve is often graphed with elastic stress amplitude on the vertical axis, other measures of load could be used, such as bending moment or force amplitude.

SN-curves for specimens where fatigue life is mainly determined by crack growth, such as welded joints, typically exhibit a steep slope (k≈3). For un-notched components the SN-curves are typically flat (k≈7 for steel).

In addition to the SN-curves as described above (Wöhler type) the so-called Bastenaire equation is sometimes used. It is written in the form

For the stresses S and SE you sometimes use the amplitudes or the maximum stresses, which are related by

where R is the R-ratio S' is the amplitude and S is the maximum stress. Both version of the Bastenaire equation have the same form. The parameters for both version are related by

Similar to the SN-curves of Wöhler type, the Bastenaire formula gives a relation N=f(S), which can be used instead of the Wöhler type curve in any fatigue calculation. However, in contrast to the Wöhler type data, the endurance limit SE does not correspond to a finite NE. The different Miner rules often used for Wöhler data do not apply to the Bastenaire data. A typical plot of the Bastenaire curve is shown in the figure below.

SN-Curve of Bastenaire Type

Specialist Durability has a provision to define the SN-curves and parameters using different ways such as Synthetic SN Curve from Strain Life and Universal Slope when you create durability materials. For more information, see Creating durability material properties.

Learn more

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

Variable amplitude loading

Stress-life analysis in Specialist Durability

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