2. Damage assessment

For a structure without geometric defects and subject to pure alternating stress, the number of cycles at break is determined from an endurance diagram, also called Wöhler curve or curve \(S-N\).

The number of cycles at break is determined by interpolation of the Wöhler curve of the material for a given alternating (one-dimensional) stress level (to each elementary cycle corresponds a stress amplitude level \(\mathrm{Ds}\text{=}\mid {s}_{\text{max}}\text{-}{s}_{\text{min}}\mid\) and an alternating stress \({S}_{\text{alt}}\text{=}1/\mathrm{2Ds}\)).

The damage of an elementary cycle is equal to the inverse of the number of cycles at break:

\(D\text{=}\frac{1}{{N}_{r({S}_{\text{alt}})}}\)

2.1. Endurance diagram

The endurance diagram, also called the Wöhler curve or curve \(S-N\) (stress-number of cycles at break curve) is obtained experimentally by subjecting test specimens to periodic force cycles (generally sinusoidal) of normal amplitude \(\sigma\) and constant frequencies, and by noting the number of cycles \({N}_{r}\) at the end of which failure occurs [R7.04.01].

The various mathematical forms of the Wöhler curve are described in the document « Estimating fatigue at large numbers of cycles », [R7.04.01] as well as how to introduce them in*Code_Aster*.

2.2. Elasto-plastic concentration coefficient

It may also be necessary to weight the stress value determined by the counting method by the elasto-plastic concentration coefficient \({K}_{e}\).

The elasto-plastic concentration coefficient \({K}_{e}\) (referred to in articles B3234.3 and B3234.5 of RCC_M [bib4]) is defined as being the ratio between the actual deformation amplitude and the deformation amplitude determined by the elastic analysis.

The value of the coefficient \({K}_{e}\) is given in document [R7.04.01].