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 :math:`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 :math:`\mathrm{Ds}\text{=}\mid {s}_{\text{max}}\text{-}{s}_{\text{min}}\mid` and an alternating stress :math:`{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:

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




Endurance diagram
---------------------

The endurance diagram, also called the Wöhler curve or curve :math:`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 :math:`\sigma` and constant frequencies, and by noting the number of cycles :math:`{N}_{r}` at the end of which failure occurs [:ref:`R7.04.01 <R7.04.01>`].

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




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 :math:`{K}_{e}`.

The elasto-plastic concentration coefficient :math:`{K}_{e}` (referred to in articles B3234.3 and B3234.5 of RCC_M [:ref:`bib4 <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 :math:`{K}_{e}` is given in document [:ref:`R7.04.01 <R7.04.01>`].