چكيده به لاتين
Geometrical discontinuities are sometimes found in engineering components. One of the important types of geometrical discontinuities is notches which can be separated depends on their geometry. One of the common types of the notches is V-notches which divide into sharp and blunt ones. Blunt V-notches are used more than the sharp ones in engineering structures, due to the existence of lower stress concentration at their root. On the other hand, to reduce the high-stress concentration at the tip of the sharp notches, stop holes are used which create a new type of notches named VO-notches. Considering the widespread use of stop hole technique for reducing the concentration of stress at the tip of cracks and sharp notches, and also common use of blunt notches in components and structures, extracting the stress field around the VO-notches and blunt V-notches seems useful.
This study presents the in-plane asymptotic displacement and stress fields in the vicinity of VO-notches and blunt V-notches based on the Muskhelishvili’s approach. In the first part, the displacement and stress components in the polar coordinate system are determined by choosing appropriate complex potential functions. Then, the notch boundary conditions are imposed to calculate the free parameters of the stress distribution. Eventually, the stress and displacement components are calculated in the Cartesian and polar coordinates in the forms of series expansions related to mode I and mode II loading. In the second part, in order to calculate the coefficients of the series, a numerical technique called the over-deterministic method is utilized. According to the over-deterministic method, the unknown coefficients are calculated by fitting the asymptotic displacement field to the nodal displacement values. To show the accuracy of the derived asymptotic stress series and the effectiveness of higher order terms, various specimens under different loading conditions for several notch geometries are modeled using finite element analysis. Finally, the obtained coefficients are used to compare the stress distribution of the truncated stress series with its relevant finite element values. The numerical results indicate that a single-term solution can lead to considerable errors, and to achieve good accuracy in the stress field calculation, one should take account of at least three terms in the stress series solution.
