Stress-Life (S-N) Approach
S-N Curve
for segment 1
Where, SS is the nominal stress range, NfNf are the fatigue cycles to failure, blbl is the first fatigue strength exponent, and SISI is the fatigue strength coefficient.
The S-N approach is based on elastic cyclic loading, inferring that the S-N curve should be confined, on the life axis, to numbers greater than 1000 cycles. This ensures that no significant plasticity is occurring. This is commonly referred to as high-cycle fatigue.
S-N curve data is provided for a given material on a MATFAT Bulk Data Entry. It is referenced through a Material ID (MID) which is shared by a structural material definition.
Equivalent Nominal Stress
Since S-N theory deals with uniaxial stress, the stress components need to be resolved into one combined value for each calculation point, at each time step, and then used as equivalent nominal stress applied on the S-N curve.
Various stress combination types are available with the default being "Absolute maximum principle stress". "Absolute maximum principle stress" is recommended for brittle materials, while "Signed von Mises stress" is recommended for ductile material. The sign on the signed parameters is taken from the sign of the Maximum Absolute Principal value.
Parameters affecting stress combination may be defined on a FATPARM Bulk Data Entry. The appropriate FATPARM Bulk Data Entry may be referenced from a fatigue subcase definition through the FATPARM Subcase Information Entry.
Mean Stress Correction
Generally, S-N curves are obtained from standard experiments with fully reversed cyclic loading. However, the real fatigue loading could not be fully-reversed, and the normal mean stresses have significant effect on fatigue performance of components. Tensile normal mean stresses are detrimental and compressive normal mean stresses are beneficial, in terms of fatigue strength. Mean stress correction is used to take into account the effect of non-zero mean stresses.
The Gerber parabola and the Goodman line in Haigh's coordinates are widely used when considering mean stress influence, and can be expressed as:
- SmSm
- Mean stress given by Sm=(Smax+Smin)/2Sm=(Smax+Smin)/2
- SrSr
- Stress Range given by Sr=Smax−SminSr=Smax−Smin
- SeSe
- Stress range after mean stress correction (for a stress range SrSr and a mean stress SmSm )
- SuSu
- Ultimate strength
The Gerber method treats positive and negative mean stress correction in the same way that mean stress always accelerates fatigue failure, while the Goodman method ignores the negative means stress. Both methods give conservative result for compressive means stress. The Goodman method is recommended for brittle material while the Gerber method is recommended for ductile material. For the Goodman method, if the tensile means stress is greater than UTS, the damage will be greater than 1.0. For the Gerber method, if the mean stress is greater than UTS, the damage will be greater than 1.0, with either tensile or compressive.
Parameters affecting mean stress influence may be defined on a FATPARM Bulk Data Entry. The appropriate FATPARM Bulk Data Entry may be referenced from a fatigue subcase definition through the FATPARM Subcase Information Entry.
FKM:
There are 2 available options for FKM correction in OptiStruct and are activated by setting UCORRECT to FKM/FKM2 or MCORRECT(MCi) fields to FKM on the FATPARM entry.
- Regime 1 (R > 1.0)
- SAe=Sa(1−M)SAe=Sa(1−M)
- Regime 2 (-∞ ≤ R ≤ 0.0)
- SAe=Sa+M*SmSAe=Sa+M*Sm
- Regime 3 (0.0 < R < 0.5)
- SAe=(1+M)Sa+(M3)Sm1+M3SAe=(1+M)Sa+(M/3)Sm1+M/3
- Regime 4 (R ≥ 0.5)
- SAe=3Sa(1+M)23+M
- SAe
- Stress amplitude after mean stress correction (Endurance stress)
- Sm
- Mean stress
- Sa
- Stress amplitude
- Regime 1 (R > 1.0) and Regime 4 (R ≥ 0.5)
- Mean stress correction is not applied M=0.0
- Regime 2 (-∞ ≤ R ≤ 0.0)
- SAe=Sa+M*Sm
- Regime 3 (0.0 < R < 0.5)
- SAe=(1+M)Sa+(M3)Sm1+M3
- SAe
- Stress amplitude after mean stress correction (Endurance stress)
- Sm
- Mean stress
- Sa
- Stress amplitude
- M
- Equal to MSS2
If all four MSSi fields are specified for mean stress correction, the corresponding Mean Stress Sensitivity values are slopes for controlling all four regimes. Based on FKM-Guidelines, the Haigh diagram is divided into four regimes based on the Stress ratio ( R=Smin/Smax ) values. The Corrected value is then used to choose the S-N curve for the damage and life calculation stage.
There are 2 available options for FKM correction in OptiStruct and are activated by setting UCORRECT to FKM/FKM2 and MCORRECT(MCi) fields to FKM on the FATPARM entry.
- Regime 1 (R > 1.0)
- SAe=(Sa+M1Sm)((1−M2)/(1−M1))
- Regime 2 (-∞ ≤ R ≤ 0.0)
- SAe=Sa+M2Sm
- Regime 3 (0.0 < R < 0.5)
- SAe=(1+M2)Sa+M3Sm1+M3
- Regime 4 (R ≥ 0.5)
- SAe=(Sa+M4Sm)(((1+3M3)(1+M2))/((1+3M4)(1+M3)))
- SAe
- Stress amplitude after mean stress correction (Endurance stress)
- Sm
- Mean stress
- Sa
- Stress amplitude
- Mi
- Equal to MSSi
- Regime 1 (R > 1.0) and Regime 4 (R ≥ 0.5)
- Mean stress correction is not applied
- Regime 2 (-∞ ≤ R ≤ 0.0)
- SAe=Sa+M2Sm
- Regime 3 (0.0 < R < 0.5)
- SAe=(1+M2)Sa+M3Sm1+M3
- SAe
- Stress amplitude after mean stress correction (Endurance stress)
- Sm
- Mean stress
- Sa
- Stress amplitude
- Mi
- Equal to MSSi
- Regime 1 (R > 1.0)
- SAe=(Sa+M1Sm)((1−M2)/((1+M2)(1−M1)))
- Regime 2 (-∞ ≤ R ≤ 0.0)
- SAe=(Sa+M2Sm)/(1+M2)
- Regime 3 (0.0 < R < 0.5)
- SAe=Sa+M3Sm1+M3
- Regime 4 (R ≥ 0.5)
- SAe=(Sa+M4Sm)((1+3M3)/((1+3M4)(1+M3)))
Damage Accumulation Model
- Nif
- Materials fatigue life (number of cycles to failure) from its S-N curve at a combination of stress amplitude and means stress level i .
- ni
- Number of stress cycles at load level i .
- Di
- Cumulative damage under ni load cycle.
The linear damage summation rule does not take into account the effect of the load sequence on the accumulation of damage, due to cyclic fatigue loading. However, it has been proved to work well for many applications.