1. Introduction#

The damage assessment is based on the use of material endurance curves, combining a variation in stresses of a given amplitude with a number of admissible cycles defined by a fatigue curve.

Material fatigue curves are established by subjecting test specimens to sinusoidal stresses of constant amplitude from the start of the test until failure.

To use these curves from a real load, it is necessary to identify cycles in the stress history, which is done by cycle counting methods. Numerous methods exist: the document [R7.04.01] presents two methods for counting cycles in the case of a real deterministic load.

However, many real mechanical loads affecting nuclear components are random, which leads to preference being given to the use of statistical methods to assess the damage suffered by these structures.

Some methods for counting stress cycles have been the subject of statistical interpretation:

  • method for counting stress peaks

  • method of counting the number of times a given level has been exceeded.

The field of application of these two methods [bib1] [bib2] is limited to random loadings that are ergodic (the analysis of a single sample is sufficient to characterize the parameters of the process) and Gaussian (the values of the measured signal are distributed according to a normal distribution) random loads.

On the other hand, the evolution of the signal is assimilated to a random process characterized by its statistical parameters (spectral moments of order 0, 2 and 4) [R7.10.01].

In both cases, the statistical event to be taken into account is simple to define:

  • a stress peak is defined by a zero slope and a negative acceleration for a positive peak, a positive acceleration for a negative peak,

  • Exceeding stress level \({S}_{0}\) is characterized by a signal value equal to \({S}_{0}\) and by a positive slope.

Since the stress cycles are known by these methods, we then move on to calculating the number of cycles at break from a fatigue curve. The Wöhler curves that are established experimentally have been approximated by various mathematical expressions that more or less correctly characterize the different areas of these curves.

Three mathematical expressions are available in*Code_Aster*: one discretized form and two analytic forms.

Knowing the number of stress cycles (given by one of these two cycle counting methods) and the associated elementary damage (determined by interpolation on the Wöhler curve of the material), it is possible to calculate an average damage over the duration of the signal.