Wohler line

The result, therefore, is that the behavior of components under dynamic pressure load is determined by so-called Wohler tests (S-N tests). Here, pressure containers during lab tests are subjected to constant pressure amplitudes Pof a certain magnitude until they finally fait. If such tests are conducted on identical components using different amplitudes until the component in question fails and the results are plotted in a double-logarithmic system of coordinates having a coordinate pressure amplitude AP and a cycle life N, then the result will be a straight line known as the Wohler line S-N line) which can be represented by the... 

This line displays a course which is component and material dependent and must thus be known beforehand if the behavior of certain components is to be evaluated. Tests have proven that the gradient of the Wohler line, e.g., for welded pipe, is = 4,5. Now the problem is to effect a combination of the information contained in the Wohler line and the operational load universe this may be achieved in the following manner. 

Assume that there is an operational load collective Af = AP(H) plus a Wohler line which can be represented by Equation (5-1). The deterioration quotient a5 of the pressure amplitudes AP of a narrow load collective range between AP H) and AP H + dH)—according to the linear deterioration hypothesis by Palmgren and Miner [5-3]—is indicated by the frequency dH of the amplitudes within that range and the cumulative number of stress cycles which the latter will sustain, namely A=C,(C2AP(//)) ... 

Here N constitutes the endurable number of stress cycles at pressure amplitude P as represented by the Wohler line. Using (5-1) will lead to the following conditional equation for the representative pressure amplitude AP ... 

Figure 5.5 Operational load collective and Wohler line.

MN.rn for Redux 775. A modified epoxy, Araldite 106, gave a Wohler line valid up to 8 x 10 cycles with an endurance limit of... 

As the ambient temperature is raised towards the Tg of the adhesive, the Wohler line is transposed downwards on the stress scale. With Araldite 106, the change is marked even over the range 20°-40° whereas Redux 775 has to be raised to 60°C before the change from 20°C is appreciable. 

In order to gain an antiserum for ferritin studies, Wohler and Schonlau (W7) injected rabbits with a 0.05 % isotonic solution of ferritin (20 % iron) at pH 7.2. Injections were made every fourth day, and 0.5, 1.0, 2.0, and (twice) 2.0 mg were given subcutaneously. The titer which was thus obtained was 1 500. If this antiserum was used in ImEl against separate sera with a content of at least 100 ng % ferritin, lines of precipitation could be stained with Berlin blue reaction. Ferritin shows a line which comes near Pi-globulin. A positive Ouchterlony test was obtained with most patients suffering from hepatitis epidemica or from liver cirrhosis. 

In 1845, for instance, Adolph Wilhelm Hermann Kolbe (1818-84), a pupil of Wohler s, succeeded in synthesizing acetic acid, an indubitably organic substance. Furthermore, he synthesized it by a method which showed that a clear line of chemical change could be drawn from the constituent elements, carbon, hydrogen, and oxygen, to the final product, acetic acid. This synthesis from the elements or total synthesis is all that can be asked of the chemist. If Wohler s synthesis of urea did not settle the matter of the vital force, Kolbe s synthesis of acetic acid did. 

It may be assumed that the sulfate ions necessary for the Wohler effect are produced from the sulfamic acid by the oxidizing power of the permanganate as shown in the above equation. It is in line with this assumption that other strong oxidants (HgOg, KCIO3 etc.) also produce sulfate and that N-alkyl and aryl derivatives of sulfamic acid behave like the parent compound in this respect. 

Fig. 1.55 Appearance of persistent slip bands broken line) in a specimen of mild steel 0.09 % C tested in reci nocating bending. Wohler curve is also shown full line) [78]...

Therefore, the Basquin line approximate the Wohler curve only in the high cycle fatigue regime, as shown in Fig. 5.15. When the plastic component of the strain cannot be neglected and this happens in general below 10" -10 cycles, the Basquin component must be integrated with the Mason-Cofi n component, as it will be shown in the next chapter. 

Once the analytical expression of the hysteresis loop has been derived, the following step is to infer the equation of the entire e-N curve or Wohler s curve. To this purpose, it is necessary to separate the two component of deformation, the elastic and the plastic one, as already done in Eq. (6.1). As to the elastic component Eg, it has been said in Sect. 5.2.2 that in 1910 Basquin [7] found a power law relationship with the cycles to failure N, see Eq. (5.22), so that in a log-log scale the elastic component of the S-N curve is a line. Later in the 50, Manson and Coffin [8-11] independently found that also the plastic component of the cyclic strain was related to life cycles N through a power law function, known as the Manson-Coffin relationship... 

Matting and Draugelates use for the actual Wohler curve, a line drawn through the mean value of the groups of replicated test pieces and point out that it becomes a straight line on a double logarithmic plot expressed by the relation ... 

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