Asymptotic stress field and the coefficients of singular and higher order terms for V-notches with end holes under mixed-mode loading

Abstract

In the present study, the asymptotic stress and displacement solutions related to mixed mode I/II loading are calculated in the vicinity of the V-notches with end holes (VO-notches). After deriving the asymptotic stress and displacement fields, 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, the Brazilian disk specimen is modeled using finite element analysis. Different examples under pure mode I, pure mode II and mixed mode I/II loading for three different notch opening angles and four notch tip radii are considered and the coefficients of stress series are computed for each example. Finally, the obtained coefficients are used to compare the stress distribution of the truncated stress series with its relevant finite element values. The results show that considering the singular terms alone will generate large amounts of errors while very good accuracy could be achieved by considering the higher order terms.