Statistical Nature of Fatigue

The basic nature of fatigue mechanism suggests that one can expect a large variation in data. Since the initiation of a crack at a point in the material will depend upon suitable combination of highest stress concentration due to local defect and level of stress alongwith larger number of cycles (how large is never certain), it is never certain after how many cycles a crack will initiate and then become unstable to cause fracture. These events will eventually depend upon the distribution of defects which is highly statistical in nature. As a consequence if several specimens are tested at a particular stress level (say at 500 MPa in Figure (a) all of them will fail after different number of cycles. This will be true of any other stress level. This creates difficulty in analyzing fatigue, for example, in plotting stress-log N curve. Normally the distribution of N or log N is considered for calculation of standard deviation and confidence level on arithmetic mean of each data set for a particular stress level. The line which is shown in Figure 38 passes through the arithmetic means and thus represents a 50% probability of failure or survival at any stress level for specified life. A number of specimens are tested at each stress level to establish stress-log N curve.
Determination of fatigue strength or limit of a material becomes still more complicated if one recognises the fatigue limit or strength as a stress level above which the material will fail and below which it will not fail. Several methods have been introduced for calculation of fatigue strength based upon statistical methods and one is illustrated in next section.