Various limit processes for evaluating stresses at crack tip and notch crown tip

Abstract

The stress at a crack tip point can be obtained in several ways. In the first way, after letting an elliptic notch become a crack, a moving point approaches the crack tip. In the second way, after letting a moving point approach the crown point of notch, the elliptic notch becomes a crack. It is found that for some particular stresses in question the finally obtained results by using two ways are different. The mentioned result is caused by change of the order of limitation for evaluating the stress. Assumed that there are two processes, one is by letting the moving point approach the crown point of elliptic notch, and other is by letting the ellipse become a crack. In the third way, the two processes are completed simultaneously. It is found that, for example, in case that a remote shear is applied to a elliptic notch of infinite plate, the shear stress at the crown point can reach an arbitrary value, provided an appropriate limit process is assumed in the third way. Similar result is found in the normal remote loading of an elliptic notch. In addition to the detail analysis, the obtained results are summarized in the form of theorem.