During classical analysis, some special methods to extract and to count the cycles from the random stress path (very often, the Rainflow method) are used and it is needed to cumulate “damage” based on some S-N diagrams and the linear Miner-Palmgreen rule or some more elaborated non linear rules. The “damage” factor (scalar or tensor) is still the object of many researches; it is impossible to measure it during the whole loading path, even if, before failure, some slight changes on the elastic properties may be experimentally detected. Moreover, the representations of the loading and the counting methods are purely based on mathematical aspects and ignore the particular mechanical behavior of the present materials in the structure. Our objective in this paper is only limited to reach a real physical approach of the multiaxial random loadings which is very easy to perform. The main idea of the approach is to find an Equivalence rule between two complex loadings relative to “Damage” which may be used as a “Quantification” or norm of any loading relative to one particular material. This rule must have the physical meaning of “damage” and allows for the construction of simple and practical cyclic radial loadings and tools for fatigue analysis or accelerated fatigue tests.

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