fatigue sn

nafems4.md

@@ -75,10 +75,10 @@ An important part of the analysis that almost always applies to nuclear power pl
 
 ## Fatigue {#sec:fatigue}
 
-Mechanical systems can fail due to a wide variety of reasons. The effect known as fatigue can create,  migrate and grow microscopic cracks at the atomic level, called dislocations. Once these cracks reach a critical size, then the material fails catastrophically even under stresses lower than tensile strength limits. There are not complete mechanistic models from first principles which can be used in general situations, and those that exist are very complex and hard to use. Instead, using an experimental approach very much like the Hooke Law experiment, the stress amplitude of a periodic cycle can be related to the number of cycles where failure by fatigue is expected to occur. For each material, this dependence can be computed using normalised tests and a family of “fatigue curves” (also called $S$-$N$ curves) for different temperatures can be obtained.
+Mechanical systems can fail due to a wide variety of reasons. The effect known as fatigue can create,  migrate and grow microscopic cracks at the atomic level, called dislocations. Once these cracks reach a critical size, then the material fails catastrophically even under stresses lower than tensile strength limits. There are not complete mechanistic models from first principles which can be used in general situations, and those that exist are very complex and hard to use. Instead, using an experimental approach very much like the Hooke Law experiment, the stress amplitude of a periodic cycle can be related to the number of cycles where failure by fatigue is expected to occur. For each material, this dependence can be computed using normalised tests and a family of “fatigue curves” like the one depicted in\ [@fig:SN] (also called $S$-$N$ curve) for different temperatures can be obtained.
 
 
-![A fatigue or $S$-$N$ curve for two steels.](SN.svg)
+![A fatigue or $S$-$N$ curve for two steels.](SN.svg){#fig:SN width=80%}
 
 It should be stressed that the fatigue curves are obtained in a particular load case, namely purely-periodic one-dimensional, which is not directly generalised to other three-dimensional cases. Also, any real-life case will be subject to a mixture of complex cycles given by a stress time history and not to pure periodic conditions. The application of the curve data implies a set of simplifications and assumptions that are translated into different possible “rules” for composing real-life cycles. There also exist two safety factors which increase the stress amplitude and reduce the number of cycles respectively. All these intermediate steps render the analysis of fatigue into a conservative computation scheme. Therefore, when a fatigue analysis performed using the fatigue curve method arrives at the conclusion that “fatigue is expected to occur after ten thousand cycles” what it actually means is “we are sure fatigue will not occur before ten thousand cycles, yet it may not occur before one hundred thousand or even more.”