A theory of fatigue Crack Propagation in sheet specimens

Abstract

An extension of the validity of a theory proposed at the Crack Propagation Symposium in Cranfield, September 1961, has been performed by introducing a new parameter, the endurance limit σ e , into the basic formula, which thus takes the form dx dN = k(σ − σ e) β . The relationship between crack length x and number of cycles N has been derived for two alternative cases, viz. constant stress cycles ( σ = constant) and constant load cycles ( σ(1 − x) = constant). In the first case the result implies that x be a linear function of N, which has amply been verified by tests under various conditions. In the second case, a quantity y, which is a function of x involving β and σ e as parameters, and N are linearly related. The successive increase in the stress amplitude produces sudden changes in the mode of failure, which can be observed in the fractured specimens and are indicated by discontinuities in the curves, if plotted on appropriate scales. The decisive influence of the stress level on the relative lengths of the different stages of propagation is demonstrated by a diagram. Results from various test series emphasize the necessity of splitting up the crack propagation period into three stages. Within each of them y is a linear function of N, provided proper parameter values are used.