Investigation on Filippi’s stress equation for V-shaped notch with rounded vertex Part II: Mode II stresses

Abstract

Previously, the applicability of Filippi’s stress equation was examined by the present author in the presence of model I stress only. It is found that Filippi’s stress equation gives a good approximation to the mode I stress field in the neighborhood of the rounded V-notch with the ratio ρ/t being finite. The present study aims to investigate the effectiveness of Filippi’s mode II stress equation. It is found that Filippi’s mode II stress equation showed a lack of accuracy in describing the stresses in the close neighborhood of the notch tip when the constant a2 is determined by the notch stress intensity factor KIIV. However, the analytical accuracy of Filippi’s mode II stress equation can be improved considerably, if the constant a2 is determined by a convenient stress value, for example the shear stress τsω|A at point A, a point away from the notch tip by 0.5ρ measured along the notch bisector. Also, with the aim to improve the accuracy of the analytical solution when KIIV is used to define a2 conveniently, Filippi’s mode II stress equation has been modified, and its accuracy was verified by comparing theoretical stress fields with numerical results of BFM. Therefore, there are two options for describing the mode II stress in the neighborhood of a rounded V-notch tip: one is to use Filippi’s mode II stress equation with a2 determined by τsω|A; the other is to use the modified formula proposed in the present paper with a2 determined by KIIV.