# Other Factors Affecting Fatigue

## Surface Condition (Finish and Treatment)

Surface condition is an extremely important factor influencing fatigue strength, as fatigue failures nucleate at the surface. Surface finish and treatment factors are considered to correct the fatigue analysis results.

^{1}

Surface treatment can improve the fatigue strength of components. NITRIDED, SHOT-PEENED, and COLD-ROLLED are considered for surface treatment correction. It is also possible to input a value to specify the surface treatment factor ${C}_{treat}$ .

In general cases, the total correction factor is ${C}_{sur}={C}_{treat}\text{\hspace{0.17em}}\xb7\text{}\text{\hspace{0.17em}}{C}_{finish}$

If treatment type is NITRIDED, then the total correction is ${C}_{sur}=2.0\text{\hspace{0.17em}}\xb7\text{}\text{\hspace{0.17em}}{C}_{finish}\left({C}_{treat}=2.0\right)$ .

If treatment type is SHOT-PEENED or COLD-ROLLED, then the total correction is ${C}_{sur}$ = 1.0. It means you will ignore the effect of surface finish.

The fatigue endurance limit FL will be modified by ${C}_{sur}$ as: $FL\text{'}=FL*{C}_{sur}$ . For two segment S-N curve, the stress at the transition point is also modified by multiplying by ${C}_{sur}$ .

Surface conditions can be defined in the Assign Material dialog, where you assign them to each part.

## Fatigue Strength Reduction Factor

In addition to the factors mentioned above, there are various other factors that could affect the fatigue strength of a structure, that is, notch effect, size effect, loading type. Fatigue strength reduction factor ${K}_{f}$ is introduced to account for the combined effect of all such corrections. The fatigue endurance limit FL will be modified by ${K}_{f}$ as: $FL\text{'}=FL/{K}_{f}$

The fatigue strength reduction factor may be defined in the Assign Material dialog and is assigned to parts or sets.

If both ${C}_{sur}$ and ${K}_{f}$ are specified, the fatigue endurance limit FL will be modified as: $FL\text{'}=FL\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}{C}_{sur}/{K}_{f}$

${C}_{sur}$
and
${K}_{f}$
have similar influences on the E-N formula through
its elastic part as on the S-N formula. In the elastic part of the E-N formula, a
nominal fatigue endurance limit FL is calculated internally from the reversal limit
of endurance N_{c}. FL will be corrected if
${C}_{sur}$
and
${K}_{f}$
are presented. The elastic part will be modified as
well with the updated nominal fatigue limit.

## Temperature Influence

The fatigue strength of a material reduces with an increase in temperature.
Temperature influence can be accounted by applying the temperature factor
C_{temp} to modify the fatigue endurance limit FL.

C_{temp} can either by assigned directly, or isothermal temperature across
the part/element set can be defined to calculate C_{temp} as referred by FKM
guidelines for elevated temperatures. The temperature defined must be in degree
Celsius.

C_{temp} at normal temperature = 1

C_{temp} at elevated temperature defined as per FKM guidelines for the
following materials is highlighted in the table below.

C_{temp} user-defined accepts a value between 0 <
C_{temp} <= 1

C_{temp} set to NONE = 1

Type | Temp. Condition | C_{temp} Factor |
---|---|---|

None** this is for materials other than the ones below |
- | = 1 |

Fine Grain Structural Steel | 60℃ < T < 500℃ | =1 - [10^{-3} x (T/℃)] |

Other Steels (other than stainless steel)** | 100℃ < T < 500℃ | =1 - [1.4*10^{-3} x (T/℃-100)] |

GS (Cast steel and heat treatable cast steel) | 100℃ < T < 500℃ | =1 - [1.2*10^{-3} x (T/℃-100)] |

GJS (Nodular Cast
Iron) GJM (Malleable Cast Iron) |
100℃ < T < 500℃ | =1 - a_{T,D} x (10^{-3} *
T/℃)^{2} |

Aluminum materials | 50℃ < T < 200℃ | =1 - [1.2*10^{-3} x (T/℃-50)] |

Material Group | GJS | GJM | GJL |
---|---|---|---|

a_{T,D} |
1.6 | 1.3 | 1.0 |

If both C_{temp} and K_{f} are specified, the fatigue endurance limit
FL will be modified as: FL' = FL ⋅ C_{temp} / K_{f}

## Scatter in Fatigue Material Data

S | 2000.0 | 2000.0 | 2000.0 | 2000.0 | 2000.0 | 2000.0 |

Log (S) | 3.3 | 3.3 | 3.3 | 3.3 | 3.3 | 3.3 |

Log (N) | 3.9 | 3.7 | 3.75 | 3.79 | 3.87 | 3.9 |

The experimental scatter exists in both Stress Range and Life data. In the
Assign Material dialog, the Standard Error of the scatter of log(N) is
required as input (`SE` field for S-N curve). The sample mean is
provided by the S-N curve as
$\mathrm{log}({N}_{i}^{50\%})$
, whereas, the standard error is input via the
`SE` field in the
Assign Material dialog.

- Standard Error of log(N) normal distribution (
`SE`in Assign Material). - Certainty of Survival required for this analysis (Certainty of Survival in the Fatigue Module context).

A normal distribution or gaussian distribution is a probability density function which implies that the total area under the curve is always equal to 1.0.

The user-defined SN curve data is assumed as a normal distribution, which is typically characterized by the following Probability Density Function:

- ${x}_{s}$
- The data value ( $\mathrm{log}({N}_{i})$ ) in the sample.
- ${\mu}_{s}$
- The sample mean $\mathrm{log}({N}_{i}^{sm})$ .
- ${\sigma}_{s}$
- The standard deviation of the sample (which is unknown, as you input only Standard Error (SE) in the Assign Material dialog).

The above distribution is the distribution of the user-defined sample, and not the full population space. Since the true population mean is unknown, the estimated range of the true population mean from the sample mean and the sample SE and subsequently use the user-defined Certainty of Survival to perturb the sample mean.

Standard Error is the standard deviation of the normal distribution created by all the sample means of samples drawn from the full population. From a single sample distribution data, the Standard Error is typically estimated as $SE=\left({\scriptscriptstyle \raisebox{1ex}{${\sigma}_{s}$}\!\left/ \!\raisebox{-1ex}{$\sqrt{{n}_{s}}$}\right.}\right)$ , where ${\sigma}_{s}$ is the standard deviation of the sample, and ${n}_{s}$ is the number of data values in the sample. The mean of this distribution of all the sample means is actually the same as the true population mean. The certainty of survival is applied on this distribution of all the sample means.

For the normal distribution of all the sample means, the mean of this distribution is the same as the true population mean $\mu $ , the range of which is what you want to estimate.

Statistically, you can estimate the range of true population mean as:

That is,

Since the value on the left hand side is more conservative, use the following equation to perturb the SN curve:

- $\mathrm{log}({N}_{i}^{m})$
- Perturbed value
- $\mathrm{log}({N}_{i}^{sm})$
- User-defined sample mean (SN curve on Materials)
- $SE$
- Standard error (SE on Materials)

**Z-Values (Calculated)****Certainty of Survival (Input)**- 0.0
- 50.0
- 0.5
- 69.0
- 1.0
- 84.0
- 1.5
- 93.0
- 2.0
- 97.7
- 3.0
- 99.9

Based on the above example (S-N), you can see how the S-N curve is modified to the required certainty of survival and standard error input. This technique allows you to handle Fatigue material data scatter using statistical methods and predict data for the required survival probability values.

## Adjustment of Single SN Curves

- Certainty of Survival
- If the certainty of survival is not 0.5 and standard error (SE) is not 0.0, an SN curve is modified by shifting SRI1 and FL.
- Surface Condition and Fatigue Strength Reduction Factor
- A factor for surface condition (Cs) and fatigue strength reduction factor (Kf) are applied to fatigue limit to modify slope of the SN curve after 1000 cycles in the following manner.
- Static Failure
- If static failure check is activated, static failure is reported when
the maximum stress is higher than
`UTS`or corrected stress amplitude is more than`UTS`x (1- R)/2, where R is a stress ratio that the SN curve is based on. The SN curve is modified so the program can report damage value 1.0 when stress amplitude is`UTS`x (1- R)/2 if`UTS`x (1-R)/2 is smaller than SRI1. Thus stress amplitude higher than S1000 reports a damage value different from the user-defined SN curve due to the modified`b0`slope in Figure 7. - Overall SN Curve Modification
- Combining factors from certainty of survival, surface condition, fatigue strength reduction factor, and static failure, the final SN curve that is used in damage calculation is depicted in Figure 8.

## Adjustment of Multiple SN Curves

- Certainty of Survival
- Uncertainty of fatigue strength of material can be taken into consideration by means of the standard error of log(stress) and certainty of survival.
- Surface Condition and Fatigue Strength Reduction Factor
- A factor for surface condition (Cs) and fatigue strength reduction factor (Kf) are applied to fatigue strength in the following manner:

## References

^{1}Yung-Li Lee, Jwo. Pan, Richard B. Hathaway and Mark E. Barekey. Fatigue testing and analysis: Theory and practice, Elsevier, 2005