# Advanced Structural Analysis/Part I - Theory/Failure Modes/Fatigue/Elementary Definitions

## Stress Cycle

The image below depicts a simple example of cyclic stress. Here, one interval has been highlighted (dotted) to illustrate a full stress cycle.

Simple example of cyclic stress history curve

The characteristics of a stress cycle are often defined in terms of its stress amplitude, max and min values, mean value and stress ratio. Sometimes additional/other parameters are used to define more subtle qualities of non-sinusoidal stress progressions. The basic properties of a stress cycle are defined below.

## Max and Min Stress of Stress Cycle

The maximum value of one stress cycle is denoted by ${\displaystyle \sigma _{fmax}}$.

The minimum value of one stress cycle is denoted by ${\displaystyle \sigma _{fmin}}$.

## Stress Range

The stress range, ${\displaystyle \Delta \sigma }$, is defined as

${\displaystyle \Delta \sigma =\sigma _{fmax}-\sigma _{fmin}}$

## Stress Amplitude

The stress amplitude, ${\displaystyle \sigma _{a}}$, is defined as

${\displaystyle \sigma _{a}={\frac {\Delta \sigma }{2}}={\frac {\sigma _{fmax}-\sigma _{fmin}}{2}}}$

## Mean Stress

The mean stress, ${\displaystyle \sigma _{m}}$, is defined as

${\displaystyle \sigma _{m}={\frac {\sigma _{fmax}+\sigma _{fmin}}{2}}}$

## Stress Ratio

The stress ratio, ${\displaystyle R}$, is defined as

${\displaystyle R={\frac {\sigma _{fmin}}{\sigma _{fmax}}}}$

## Fatigue Life

The fatigue life, ${\displaystyle N_{f}}$, is defined as the number of stress cycles, of uniform characteristics, that a specimen can endure before fatigue failure. The definition of fatigue failure varies, but it may refer to the transition from the initiation period to the crack growth period.

## Fatigue Limit

There have been strong indications that a stress amplitude threshold, ${\displaystyle \sigma _{f}}$, exist such that ${\displaystyle N=\infty }$ when ${\displaystyle \sigma _{a}<\sigma _{f}}$. This streess amplitude, ${\displaystyle \sigma _{f}}$, is referred to as the fatigue limit. It has been found however, that the fatigue limit may not exist in an absolute sense and that it can be greatly influenced by the mean stress and environmental factors.

## Nominal Stress

"A stress in the parent material or in a weld adjacent to a potential crack location calculated in accordance with elastic theory excluding all stress concentration effects". -the definition of nominal stress according to EN 1993-1-9.

Note that the nominal stress may correspond to different measures of stress, such as: normal stress, shear stress and equivalent stress.