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

- 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 at evaluating stresses generated in a rounded V-shaped notch with a finite depth.
- 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.
- Filippi's equation is also effective in evaluating the stresses along direction of θ≠0, however, as θ increases, the discrepancy between Filippi's equation and the numerical analysis becomes larger. It is advisable to limit calculation points of stress within a range of θ≤30°.
- 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.

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.