Fatigue (material)#The S-N curve
The SN test and fatigue test and the SN curve are terms from materials engineering. Your application can be found in the operating strength, an area in the field of mechanical engineering. It is named after August Wöhler, the 1858-1870, the first methodological fatigue strength tests performed ( Niederschlesisch - märkische railway in Frankfurt ( Oder) ).
Wöhler test
The SN test is the fatigue strength, more precisely determined the fatigue strength and fatigue strength of the materials or components (component Wöhler test). For this, the test specimens are cyclic, usually loaded under a sinusoidal load-time functions. The load amplitude and the voltage ratio under load to the upper load are constant.
To determine the values of the test specimens are tested for several load horizons. The SN test runs until a defined failure (breakage, crack initiation ) occurs or a specified number of oscillations ( number of cycles ) is over. Test specimens that reach the limit number of cycles without any apparent failure are referred to as completers.
SN curve or curve
The results of the experiment you wear in a chart. Typically, the nominal stress amplitude Sa is plotted linearly or logarithmically on the number of cycles shown logarithmically, tolerable in the Wöhler diagram. The resulting curve is called the Wöhler curve or Wöhler curve. In the adjacent SN curve the three regions K, Z and D are registered.
- K is the field of short-term strength or short- cycle fatigue (English low cycle fatigue, LCF) below approximately 104-105 load cycles. This type of fatigue occurs at high plastic Dehnamplituden that lead to early failure. To represent this area in more detail, the Coffin - Manson plot is used in the rule. At a load that leads within a quarter of cycles to failure, it is called the static strength, which is also determined in the tensile test.
- Z is the range of fatigue strength or fatigue life of between 104 and depending on the material is about 2 x 106 load cycles in which the SN curve nearly straight runs at doppellogarithmischer representation. The straight line can be described by the equation Basquin.
- D is the subsequent area of the so-called fatigue strength. For ferritic- pearlitic steels of the fatigue strength range starts at about 1-5 x 106 However, it is controversial today, whether there is a real fatigue strength or whether it at very high numbers of cycles ( engl. very high cycle fatigue, VHCF ) even at very low loads to failure comes. When austenitic steels and base materials with face-centered cubic crystal lattice (eg, aluminum, gold, copper ) the tolerable amplitude to drop. A "real" endurance limit does not exist here. Therefore, the tolerable amplitude at 108 load cycles is here usually referred to as fatigue. Where a permanent component corrosion or highly elevated temperatures, so can not be expected to fatigue strength.
Interpretations
Below the fatigue strength SaD can endure a lot of load cycles a component in principle arbitrary. Stresses above the fatigue strength cause failure of the component after a certain number of load cycles. The number of endured load cycles of a component under operating load ( variable load amplitudes) to failure can be predicted within the framework of statistical accuracy with the help of the SN curve. For this we use the methods of linear damage accumulation according to Palmgren, Langer and Miner. This is known as fixed operational assessment of a component. Fatigue is employed in almost all areas of technology for the purpose of lightweight construction.
The scatter of the measured results of the SN test is strikingly large. It comes only slightly from inadequacies of the trial, but mainly of divergent material properties within the components. She obeys the extreme value theory by W. Weibull and Gumbel EJ namely the distribution of the strengths of the smallest volume elements ( Weibull distribution ). From the extreme value theory and the statistical size effect follows: Small components have on average a higher fatigue strength than large of identical material. However, large, small, notched and unnotched components have a common lower limit of endurance: the zero line of fracture.
An extended, spatial Wöhler diagram with the axes: stress amplitude, number of cycles to fracture probability and is mathematically described with a scatter band function ( SBF ). This SBF has six constants are determined from the chart, and the SN level variation of the fatigue strength. The most important result from the SBF is the zero line of fracture, whose probability is adjusted individually using the confidence intervals (eg, 1 ppm, 10 ppm). This evaluation of the single-stage SN experiment, it is also possible to make statistically valid statements about the development of the multi-stage fracture probability under operating load. Influences of the medium voltage can be taken into account that are not of interest, such as temperature or corrosion.