6.4. Fatigue failure model#

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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:

\[ g\left( D_{cr}, A, \text{SSF}, \Theta \right) = D_{cr} - \Theta \cdot 10^{- A} {\text{SSF}}^{B} \sum_{j = 1}^{k}{N_{j} {S_{eq,j}}^{B}}, \]

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.

Table 6.4.1 Input variables for reliability analysis#






Threshold for accumulated damage




S/N curve slope




S/N curve intercept




Global stress scaling factor




Load collective distribution




Number of load cycles




Model uncertainty


uncertain 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.


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