Deriving stress-cycle (Woehler) diagram from Weibull evaluation

The prerequisite for the failure points within a curve in the Weibull diagram is that they are all subject to the same loads. In contrast, in the stress-cycle (Woehler) diagram, the running time or alternating load cycles is represented as a function of the component load (ordinate). A statement can be made with regard to the expected service life under a certain load. On the other hand, a statement cannot be made as to what percentage of the components will fail under a certain load. This is, however, possible through the combination of Weibull evaluation and stress-cycle (Woehler) diagram. At a certain failure frequency, e.g. 50 %, the point in the Weibull diagram is projected downward to the stress-cycle (Woehler) diagram for each load case. The Woehler line can be drawn by connecting these points. In the same way, a probability range can be created in the stress-cycle (Woehler) diagram for a certain range, e.g. 5 %, 95 % failure frequency.

In practical applications, it can be seen that the Weibull gradients under various loads differ as they are also subject to random scatter. Since the 5 % and 95 % lines are directly dependent on the rise in the Weibull curves, this results in either expanding or tapering ranges in the stress-cycle (Woehler) diagram. A greater "absolute" scatter of the test results can be expected at higher alternating load cycles (running times at lower loads). This comes about, however, not only through an expanding (widening) range but also in a range with a parallel progression due to the logarithmic scale. In view of the same test conditions, as already described, the rise rates should essentially not differ. It is therefore recommended to use a mean rise b in the stress-cycle (Woehler) diagram to determine the 5 % line and 95 % line. These lines then run parallel to the 50 % line and should not be confused with the lines described with the confidence range.

This representation is, of course, only possible for the fatigue strength range for finite life. The fatigue endurance strength range, as is typical for steel components and at which the Woehler line changes to a horizontal, cannot be determined as in this case failure no longer occur. Since certain materials more or less always have a certain fatigue strength range at higher running times or alternating load cycles, when evaluating materials with unknown characteristics, as many "load points" as possible should be checked in order to determine the kink in the curve.

This methode can be used in the template Weibull_Woehler.vxg