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

Abstract

In the present paper, in order to investigate systematically the effectiveness of Filippi’s stress equation applied at evaluating stresses generated in a rounded V-shaped notch with a finite depth, the stresses generated in a semi-infinite plate with rounded V-shaped notch subjected to a uniform tension load at remote are used as a base data to examine the applicability of Filippi’s stress equation. It is found that Filippi’s equation gives an excellent approximation to the stresses along the notch bisector for rounded V-shaped notches. The generalized stress intensity factor Kρ,IV(r) is almost constant along the notch bisector in the region where the stresses are governed by the singular stress field in a sharp notch; the peak discrepancy between Filippi’s equation and the numerical analysis is less than 7% when the notch opening angle γ=0°,2.5% when γ=30° and 5% when γ=90° and 120°. Also it is found that Filippi’s equation is effective in evaluating the stresses along direction different from the notch bisector, however, as the calculation angle θ with respect to the notch bisector increases, the discrepancy between Filippi’s equation and the numerical analysis becomes larger. Therefore, it is advisable to limit calculation points of stress within a range of θ⩽30°. Moreover, values of the maximum stress σmax predicted by various techniques are also examined using the numerical-analysis results of the semi-infinite plate with a V-shaped notch, and an analytical approach for predicting the constant a1 in Filippi’s equation is proposed.