On the New Damage Line in the Fatigue of Metals

The concept of the damage line, which is first proposed by H.J. French, is frequently quoted to discuss the problem on the fatigue of metals. For example, this line is illustrated in the German Industrial Standard DIN 50 100 on the fatigue. In the case of treating the fatigue strength of materials, it seems reasonable to estimate the degree of the damage by the effect of overstress on the endurance limit. But, in the design of practical machines or structures, these components are not necessarily designed for the purpose of eternal use; in other words, not only understress but overstress higher than the endurance limit may apply to these parts. Therefore, the authors pointed out that the French's damage line is judged by the decrease of the endurance limit.When the material is subjected to the repeated stress higher than the endurance limit, the estimation of the damage should not be judged by the damaging effect on the endurance limit but it is the most valid to judge the damage by the effect on the fatigue life for the repeated stress above the endurance limit. The new damage line proposed here is that one in which the estimation of the damage is based on the fatigue life and it will be the basis of predicting the fatigue life under the repeated stress with varying amplitude.In this paper, we illustrated several examples of the new damage line practically obtained from the results of the fatigue tests in which subsequent two stress levels apply to the material. Three kinds of carbon steel were used as the test materials. The judging stress for damage (the secondary stress) is the 10% overstress higher than the endurance limit. The degree of damage D is calculated by the following expression:where N0 is the number of cycles to fracture of the virgin material under the judging stress level and Nf is the number of cycles to fracture of the prestressed material under the same stress level.As the results of experiments, it has been also found that this newly proposed damage line is very different in its shape from the French's one.