# Fatigue failure model

## Contents

# 6.4. Fatigue failure model#

## 6.4.1. Model description#

Fatigue is a failure mechanism incurred by cyclic loading, leading to the initiation and extension of cracks, which degrade the strength of materials and structures. We consider here case of high-cycle fatigue failure, i.e., failures that occurs after a modelled component is exposed to large numbers of load cycles. The limit state function for this type of failure can be written as:

This expression contains a set of variables that we consider uncertain (\(D_{cr}, A, \text{SSF}, \Theta\)) and parameters that we consider to be known with a sufficiently high accuracy (\(B, \{S_{eq,j}, N_j\}_{j=1,\cdots,N}\)). A summary of these variables and their meaning is given in Table 6.4.1.

Name |
Description |
Unit |
Type |
---|---|---|---|

\(D_{cr}\)/D_cr |
Threshold for accumulated damage |
\(-\) |
uncertain |

\(A\)/A |
S/N curve slope |
\(\log(N/m^2)^{-1}\) |
uncertain |

\(B\)/B |
S/N curve intercept |
\(-\) |
deterministic |

SSF |
Global stress scaling factor |
\(-\) |
uncertain |

\(S\)/S |
Load collective distribution |
\(N/m^2\) |
deterministic |

\(N\)/N |
Number of load cycles |
\(-\) |
deterministic |

\(\Theta\)/Theta |
Model uncertainty |
\(-\) |
uncertain |

### 6.4.1.1. Load collective#

The load collective is the set of load events that the component was subjected to during its lifetime. The collective is denoted here by \(\{S_{eq,j}, N_j\}_{j=1,\cdots,N}\). To simplify usage of this interactive tool, the user can specify a distribution from which the load collective is sampled and a number of total load cycles \(N\). The generated distribution is then shown in a plot after the analysis.

## 6.4.2. Interactive reliability prediction#

This page offers an interactive reliability prediction that lets the user specify the properties of all variables listed in Table 6.4.1. The value of **deterministic variables** can be selected with a slider. **Uncertain variables** are characterized by:

*Distribution*denoted by “Dist” and can be choosen from a set of parametric probability distributions;*Mean*value denoted by “E” and can be selected with a slider;*Coefficient of variation*denoted by “C.o.V.” and can be selected with a slider.

Note

To run the interactive reliability prediction on this page, click the –> Live Code button on the top of the page. Wait a few seconds until the Kernel has loaded and run the cell below with Run.

```
from nrpmint.booktools import fatigue_failure
# start the web user-interface
fatigue_failure.web_ui()
```