The s-n curve, also called the Wöhler curve, are obtained through a series of tests where a specimen "Specimen (mechanical)") of the material is subjected to cyclic stresses with a relatively large maximum amplitude (approximately 2/3 of the static tensile strength). The cycles until failure are counted. This procedure is repeated in other specimens at decreasing maximum amplitudes.
The results are represented in a stress diagram, S, against the logarithm of the number N of cycles until failure for each of the specimens. S values are normally taken as voltage amplitudes.
Two types of S-N curves can be obtained. The higher the tension, the lower the number of cycles until failure. In some ferrous alloys and titanium alloys, the S-N curve becomes horizontal for large values of N, that is, there is a limiting stress, called the fatigue limit, below which fatigue failure will not occur.
It is often said, in a very superficial way, that many non-ferrous alloys (aluminum, copper, magnesium, etc.) do not have a fatigue limit, since the S-N curve continues to decrease with increasing N. According to this, fatigue failure will occur regardless of the magnitude of the maximum applied stress, and therefore, for these materials, the fatigue response would be specified by the fatigue resistance, which is defined as the level of stress that produces failure after a certain number of cycles. However, this is not accurate: it is naive to believe that a material will break after so many cycles, no matter how ridiculously small the stress present.
Strictly speaking, all crystalline materials (metals,...) have a fatigue limit. It happens that for materials such as most ferrous materials, this limit is usually around one million cycles (for rotating specimen tests), for internal stresses that are around 0.7-0.45 times the elastic limit of the material; while for those that say they have no fatigue limit, such as aluminum, it occurs even for very low stresses (in aluminum, 0.1-0.2 times said limit), and appears at very high cycles (in aluminum it can reach one billion cycles; in titanium it can be, depending on alloys, one hundred million cycles or even, exceptionally, one billion cycles). As in general machines or elements are not designed so that the maximum stresses are 0.1-0.2 times the elastic limit of the material, since in that case a good part of the mechanical capabilities of the material would be wasted, and as it is not usually designed assuming life values above one million cycles, in practice these types of materials will not be able to present their fatigue limit, although they do have it.
This confusion arises from the very nature of Wöhler's S-N curves, which were conceived in the century for steels. When the type of metallic materials common in engineering was expanded, the same concepts and the same curves were transferred to other metals whose fatigue behavior is essentially different (in fact, the great variability of behavior that it presents in the different types of materials is a characteristic of fatigue). And since steel has been and is the cornerstone of engineering, it was interesting to compare the properties of other metals with respect to it: it is and was common that, when testing materials, the tests were suspended once the million cycles had passed, considering that it was not interesting to characterize materials above that time limit.
Another important parameter that characterizes the fatigue behavior of a material is the fatigue life N. It is the number of cycles to produce a break at a specified stress level.[4].
Furthermore, knowledge of fatigue behavior is not the same for all materials: the best known, most tested and most reliable material in terms of fatigue predictions is the steel family. For other commonly used metallic materials such as aluminum, titanium, copper, nickel, magnesium or chromium alloys, less information is available (this decreases with the novelty of the alloy), although the shape of the fatigue calculation criteria and the S-N curves seems regular, and is similar to that of steels, and its reliability is considered to be high. For ceramic materials, on the contrary, very little information is available, and in fact, the study of fatigue in them and in polymers and composite materials is a hot topic of current research.
In any case, there is a notable difference between theory and reality. This leads to significant design uncertainties when fatigue life or fatigue limit are considered. The scatter in results is a consequence of the sensitivity of fatigue to various test and material parameters that are impossible to control precisely. These parameters include the manufacture of the specimens and the preparation of the surfaces, metallurgical variables, alignment of the specimen in the testing equipment, average stress and test loading frequency.
Approximately half of the specimens tested break at stress levels that are about 25% below the curve. This is usually associated with the presence of sources of internal stress concentration, such as defects, impurities, notches, scratches,..., which have remained undetected.
Statistical techniques have been developed and used to handle this failure in terms of probabilities. A convenient way to present results treated in this way is with a series of constant probability curves.