<jupyter_start><jupyter_text>Fatigue failure model Go to handbook  Model descriptionFatigue 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 {numref}`fatigue_model_inputs_table`.```{list-table} Input variables for reliability analysis:header-rows: 1:widths: 15 45 20 20:name: fatigue_model_inputs_table* - 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``` Load collectiveThe 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. Interactive reliability predictionThis page offers an interactive reliability prediction that lets the user specify the properties of all variables listed in {numref}`fatigue_model_inputs_table`. 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 {fa}`rocket` --> {guilabel}`Live Code` button on the top of the page. Wait a few seconds until the Kernel has loaded and run the cell below with {guilabel}`Run`.``````{admonition} Under construction:class: todoThe numerical values and bounds for the input variables are not finalized yet. Therefore, computed failure probabilities might not be representative of the considered components.```<jupyter_code>from nrpmint.booktools import fatigue_failure

# start the web user-interface
fatigue_failure.web_ui()<jupyter_output><empty_output>
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